There are several different constructions that can be used when comparing one thing to another. 

Comparatives (More than/Greater than)

The idea of something being more or greater than something else (comparative) is expressed by means of a construction which can be represented by the following formula:

A Q law' B Q puS

In this formula, A and B are the two things being compared and Q is the quality which is being measured. The two Klingon words in the formula are law' be many and puS be few. Thus, it says A's Q is many, B's Q is few or A has more Q than B has or A is Q-er than B. 

Any verb expressing a quality or condition may fit into the Q slot.

la' jaq law' yaS jaq puS The commander is bolder than the officer.
(la' commander, jaq be bold, yaS officer)

tlhIngan qu' law' tera'ngan qu' puS the Klingon is more fierce than the Terran
(tlhIngan Klingon, qu' be fierce, tera'ngan Terran)

Superlatives (most)

To express the superlative, that something is the most or the greatest of all, the noun Hoch all is used in the B position:

la' jaq law' Hoch jaq puS The commander is boldest of all.

tlhIngan qu' law' Hoch qu' puS the Klingon is the fiercest of all.

In comparative and superlative constructions, the verb of quality (jaq be bold in the sentences above) must be said twice.

Same as/Identical

There are a few ways to express this idea. 

The most common ways to express "A is as Q as B," involve constructions which parallel the law'/puS construction for comparatives and superlatives as described above.

If the quality being discussed is the same for both A and B, that is, if A and B are the same as far as Q goes, there are a number of options.

The most frequently heard, and most neutral, construction is A Q law' B Q rap, as in:

tlhIngan woch law' tera'ngan woch rap the Klingon is as tall as the Terran
(woch be tall)

While, in theory, it is possible to use the same construction with puS instead of law' (that is A Q puS B Q rap), this is seldom done and when it is done, there is a connotation of disparagement. 

A variant of this construction uses nIb instead of rap:

tlhIngan woch law' tera'ngan woch nIb the Klingon is as tall as the Terran

nIb implies precision (the Klingon and the Terran are that exactly as tall as each other) and is not likely to be used unless the quality being discussed is quantifiable or measurable. rap, on the other hand, may be used regardless of whether the quality is quantifiable.

It should be noted that this restriction on nIb applies only in this sort of construction. It is perfectly natural to say, for example, nIb va'nuchDu'chaj "their heels are identical" (va'nuch heel, -Du' plural, -chaj their) without suggesting in what way they are identical and without implying that any precise measuring has or has not occurred or could or could not occur.

Another way to express the notion of "A is as Q a B" is by attributing the quality in question to A and saying that B is the same, that is, Q A, rap B "A is Q, B is the same" (rap be the same), though the translation into English is usually "H is as Q as A," For example:

ghun 'Iw HIq, rap boqrat chej the bokrat liver is as warm as the bloodwine

literally, "The bloodwine is warm, the bokrat liver is the same" (ghun be warm, 'Iw HIq bloodwine, boqrat bokrat, chej liver).

'ey ro'qegh'Iwchab, rap qagh the gagh is as delicious as the rokeg blood pie

literally, "The rokeg blood pie is delicious, the gagh is the same" ('ey be delicious, ro'qegh'Iwchab rokeg blood pie, qagh gagh).

It is also possible to use nIb be identical rather than rap. For example:

'ugh ro'qegh'Iwchab, nIb raHta'
the racht is as heavy as the rokeg blood pie

literally, "The rokeg blood pie is heavy, the racht is identical" ('ugh be heavy, raHta' racht).

Using nIb in this kind of construction, as with the law'/puS construction, carries a connotation of preciseness -- the rokeg blood pie -- and the racht are exactly the same weight. Thus, it might be used when referring to something that can be measured, such as weight, but it is not likely to be used with less quantifiable qualities where the assertion of sameness is more a judgment, such as deliciousness. It is never improper to use rap even in cases where the quality is measurable.

If the quality being discussed is a positive one, or if having the quality is a positive attribute, another (similar) construction may be used: A Q law' B Q law'. Likewise, if the quality is a negative one, or if having the quality is considered a negative attribute, one may use the construction A Q puS B Q puS. Compare:

ro'qegh'Iwchab 'ey law' qagh 'ey law' the rokeg blood pie is as delicious as the gagh

'Iw HIq bIr puS chuch bIr puS the bloodwine is as cold as the ice is (or, the bloodwine is as cold as ice)
(bIr be cold, chuch ice)

Being delicious is a good thing as applied to food, so using law' twice emphasizes just how delicious the two dishes are. On the other hand, bloodwine is best when served warm. Using puS twice emphasizes how inappropriate the coldness of the bloodwine is. (It is not likely even cold bloodwine is really as cold as ice, but a disgruntled Klingon is not beyond hyperbole.)

It should be pointed out that although these constructions may be used to form similes, they are generally used only when comparing similar things. Commonly, a simile (where two basically unlike things are compared) is of the form Q A; B rur (rur resemble) (thus, A resembles B with regard to a particular quality, Q, though otherwise A and B would probably not even be compared). For example:

puj verengan; bIQ rur the Ferengi is as weak as water
(puj be weak, verengan Ferengi bIQ water)

literally, "The Ferengi is weak; he/she resembles water."

When the law'/rap, law'/law' or puS/puS constructions are used to compare unlike things, they generally make reference to (or, better, are recastings of) well-known similes. Some examples:

Compare these two sentences:

SuvwI' ghung law' qagh ghung rap the warrior is as hungry as gagh
(SuvwI' warrior, ghung be hungry)

ghung; qagh rur hungry as gagh

Compare these two sentences:

tlhIngan HoS law', 'Iw HoS law' the Klingon is as strong as blood
(HoS be strong, 'Iw blood)

HoS; 'Iw rur strong as blood

Compare these two sentences:

verengan puj puS, bIQ puj puS the Ferengi is as weak as water

puj; bIQ rur weak as water

Not the same as

To express the opposite notion, that is "A is not as Q as B," the most common locution is A Q law' B Q pIm (pIm be different), as in:

QuchlIj vIl law' QuchwIj vIl pIm your forehead is not as ridgy as my forehead
(Quch forehead, -lIj your, vIl be ridgy, -wIj my)

Here is an instance where the English translation does not properly capture the Klingon meaning. The English "your forehead is not as ridgy as my forehead" implies (though it does not explicitly state) that my forehead is ridgier than yours. This implication is not in the Klingon. QuchlIj vIl law' QuchwIj vIl pIm means only that the ridginess of your forehead and mine is not the same. If the intended meaning is what the English implies, one would use the normal law'/puS construction:

QuchwIj vIl law' QuchlIj vIl puS my forehead is ridgier than your forehead

To disagree with this notion, that is, to assert that your forehead is not ridgier than mine (it may be less ridgy, or the ridginess may be the same), one would use the construction A Q law'be' B Q puSbe' (A's Q is not many, B's Q is not few) (-be' not):

QuchlIj vIl law'be' QuchwIj vIl puSbe' your forehead isn't ridgier than my forehead

More on law'/puS

You can definitely use the law'/puS formula as part of a longer sentence. In these examples note that the non-comparative part - which is marked with [square brackets] - usually appears as a sort of prologue, place stamp or dependent clause to the actual comparative:

[jonlu'meH] wo'maj pop tIn law' Hoch tIn puS 
Our Empire's highest bounty has been placed on his head.

[reH latlh qabDaq] qul tuj law' Hoch tuj puS 
The fire is always hotter on someone else's face.

[qIbDaq SuvwI"e'] SoH Dun law' Hoch Dun puS 
You would be the greatest warrior in the galaxy.

[tlhutlhmeH] HIq ngeb qaq law' bIQ qaq puS 
Drinking fake ale is better than drinking water.

[noH ghoblu'DI'] yay quv law' Hoch quv puS 
In war there is nothing more honorable than victory.

[tlhIngan wo' yuQmey chovlu'chugh] Qo'noS potlh law' Hoch potlh puS 
The principal planet of the Klingon Empire, Qo'noS...

[DujvamDaq] tlhIngan nuH tu'lu'bogh pov law' Hoch pov puS 'ej [DujvamDaq] 'op SuvwI' tu'lu'bogh po' law' tlhIngan yo' SuvwI' law' po' puS
It [IKV Pagh] has the best weapons and some of the finest warriors in the Klingon fleet.

This last one looks complicated, but it just uses long-ish noun phrases in the A and B slots of the A Q law' B Q puS formula.

As a form of word play, antonyms (that is, words with opposite meanings) other than law' and puS are sometimes plugged into the formula. The resulting phrases literally make no sense at all, but because of the uniqueness of the law'/puS phrases within Klingon grammar, they are always understood. Constructions such as the following might be heard, all meaning, though not literally, "The Klingon is braver than the Ferengi":

tlhIngan yoH HoS verengan yoH puj.
(HoS, "be strong"; puj, "be weak")

tlhIngan yoH pIv verengan yoH rop.
(pIv, "be healthy"; rop, "be sick")

tlhIngan yoH Daj verengan yoH qetlh. 
(Daj, "be interesting"; qetlh, "be dull")

Such fanciful use of words is found with the superlative construction (something is the most or the best) as well. In the superlative, the noun Hoch ("all") fits into the B slot, as in the normal sentence tlhIngan yoH law' Hoch yoH puS ("Klingons are the bravest of all"). It is possible, however, for rhetorical effect, to say such things as tlhIngan yoH HoS Hoch yoH puj (HoS, "be strong"; puj, "be weak").

If one state of affairs is not inherently better or worse than its opposite, the terms may occur in either order. Once again comparing the brave Klingon and the not-so-brave Ferengi:

tlhIngan yoH jen verengan yoH 'eS or tlhIngan yoH 'eS verengan yoH jen
({jen,} "be high"; {'eS,} "be low")

tlhIngan yoH ghegh verengan yoH Hab or tlhIngan yoH Hab verengan yoH ghegh
(ghegh, "be rough"; Hab, "be smooth")

Some conditions, on the other hand, are more highly regarded than others. In those instances, it is essential to get the terms in the correct order. For example, among Klingons, a task that is difficult (Qatlh) is more highly valued than one that is easy (ngeD). Accordingly, in these creative comparative and superlative constructions, Qatlh is associated with the quality that is "many" and ngeD with the quality that is "few." To say "The Klingon is braver than the Ferengi," one would have to say tlhIngan yoH Qatlh verengan yoH ngeD. Reversing the order of Qatlh and ngeD would produce the phrase tlhIngan yoH ngeD verengan yoH Qatlh, which, if interpretable at all, would mean "The Klingon is less brave than the Ferengi." Even if one really meant it, uttering such a phrase could lead to unfortunate consequences.

Some speakers of Klingon never use such nonconformist constructions. Some use a few from a stock set. Others seem to be somewhat creative. Among Klingons, there is a fine line between creative use of the language and silliness, however, and Klingons are rather intolerant of the latter. Accordingly, the visitor to a Klingon planet is advised to avoid making such constructions until he or she is very well versed in Klingon culture. Not only will this preclude being viewed as less than serious, it will also prevent inadvertently making comparisons backward.