Comparisons in Japanese language can be made with a couple of different constructs.

Two of the simplest are "yori" and "no hou ga". The meaning of "yori" can simply be put in English as the construct "is less than", and "no hou ga" can be simply put as "is more than". The constructs can be used separately or even be put together if wanting to be very clear. The word "hodo" can also be used in comparisons.

Other ways of comparing or showing how things relate is to say that something is number one - ichiban.

To say the word compare in Japanese you can use the word 比べる,  kuraberu.

のほうが　- No hou ga 

No hou ga is put after the word that fits the description best in comparison.

寿司のほうが好きです。
Sushi no hou ga suki desu.
I like sushi better.

僕のほうがいいです。
boku no hou ga ii desu.
I am better.

より - Yori 

Yori is put after the word that is not considered to be fitting the description as good as the alternative.

A は B より赤いです。
A wa B yori akai desu
A is more red than B. (Litt: Regarding A, B is less red)

パンは焼肉より安いです。
Pan ha yakiniku yori yasui desu
Bread is cheaper than yakiniku. (Litt: Regarding bread, yakiniku is less cheap)

カナダは日本より大きいです。
Kanada wa Nihon yori oukii desu.
Canada is larger than Japan.

日本よりカナダは大きいです。
Nihon yori Kanada wa oukii desu.
Canada is larger than Japan.

日本よりカナダのほうが大きいです。
Nihon yori Kanada no hou ga oukii desu.
Canada is larger than Japan.

Hodo

Hodo is put before a word to state that it is more suitable/correct in the comparison.

日本はカナダほど大きくないです。
Nihon wa Kanada hodo ookikunai desu.
Japan is not as large as Canada. 

Ichiban 

Ichiban 一番 is the Japanese counter for ordinal numbers, i.e. when saying in which order things come. When using ichiban, you state the one that is first and foremost in the comparison. 

 このスーパーは一番安いです。
Kono suupaa ha ichiban yasui desu.
This is the cheapest supermarket.

トラコはねこの中で一番可愛いです。
Torako wa neko no naka de ichiban kawaii desu.
Torako is the most beautiful of all cats.

トラコはエドモントンで一番可愛いです。
Torako wa Edomonton de ichiban kawaii desu.
Torako is the most beautiful (cat) in Edmonton.

Comparison in Questions

When asking someone to compare things, you can simply line up the alternatives and add "which one is ___?" in the end. 

カナダと日本とではどちらが大きいですか。
Kanada to Nihon to dewa dochira ga oukii desu ka.
Which is larger, Canada or Japan?

ねずみと犬とではどちらが可愛いですか。
Nezumi to inu to dewa dochira ga kawaii desu ka.
Which are the more attractive, mice or dogs?