"Comment" means how, and that is an adverb; it is mainly used to ask how something is done.
"Comme" means like, and that is both an adverb and a conjunction; however, it is mainly used as a conjunction to compare things.
Comment voudrais-tu le faire? Comme ça.
HOW would you like to do it? LIKE that.
Keep in mind that "comment" and "comme" have many other uses. They are not just used to compare things or to ask how something is done.
Here is an example for each of them.
Comment? Peux-tu répéter s'il te plaît?
SORRY, could you say that again, please?
Here "comment" is used so that the person repeats something or to express that you haven't understood something.
Gentille comme elle est, elle l'acceptera.
Kind AS she is, she will accept it.
Here "comme" shows the degree of intensity.
À quel point est-elle gentille? Elle est gentille COMME jamais.
To what extent is she kind? She is kind AS ever.
Hope that helps.