Use comparatives when comparing two of anything. Use superlatives when comparing three or more of anything, but only focus on one.
Comparing with adjectives
Most comparative adjectives can be formed by adding -er to the end of the word followed by than, as in big>bigger or small>smaller.
My shoes are bigger than yours. My brother is taller than me. This shirt is prettier than the other one. (change the y in pretty to i before adding -er)
Most superlative adjectives can be formed by adding -est to the end of the word, such as big>biggest or small>smallest. We also add the article the right before the word. Do not use than with superlatives.
His shoes are the biggest. My sister is the tallest. This tree is the prettiest.
If the word has three or more syllables, you cannot add -er or -est to the end of the word. You must add the word more for comparatives and most for superlatives. For example, beautiful becomes more beautiful or the most beautiful, not beautifuler or the beautifulest.
This car is more expensive than the one we looked at yesterday. Mr. Charles is the most difficult client I've ever had to deal with.
Irregular adjective forms
good > better > the best bad > worse > the worst
Comparing with nouns
When you are comparing two nouns, use more and less/fewer. When comparing three or more nouns, use the most and the least/the fewest. Use less/the least for uncountable nouns and fewer/the fewest for countable nouns. Read this article for a refresher on countable and uncountable nouns.
There are more chairs in this room than the one across the hall. This room has the most people in it. There's less water in this cup than that one, so it must be mine. This balloon has the least air in it. I made fewer mistakes on this test than my last one.
Comparing with adverbs
When comparing with adverbs, use more...than/the most and less...than/the least.
I speak English more fluently than I speak French. Your son works the most quietly in class.
There are some adverbs that do not end in -ly. When using these adverbs, add -er or -est to the ending.
My dog runs faster than your dog. Richard Jenson arrived the latest to the meeting.
Irregular adverb forms
badly > worse > the worst well > better > the best hard > harder > the hardest
Equality and Inequality
When the comparison is focused on whether the two items are equal, use as…as or not as…as. You cannot use as…as with superlatives.
Georgia is as hot as Alabama in the summer. Georgia is not as hot as Texas in the summer.
Peter runs as fast as Paul. Peter does not run as fast as John.
Use many for countable nouns and much for uncountable nouns.
There aren't as many people in this session as there are in the one across the hall. I don't have as much money to buy new clothes as you.