You should use the comparative form of an adjective to compare exactly two things. You can form the comparative by adding the suffix "-er" to the modifier (for some short words) or by using the word "more" with the modifier:
Now that it is March, the days are getting longer. (longer now than before)
You should use the superlative form to compare three or more things. You can form the superlative by adding the suffix "-est" to the modifier orby using the word "most" with the modifier:
This is definitely the most beautiful and cheapest car I have ever seen

To form the comparative and superlative forms of adjectives we must take into account the number of syllables it has. The general rules to form the comparative and the superlative of adjectives are as follows:

1. One-syllable adjectives
- Most one-syllable adjectives add suffix –er to form the comparative and –est to form the superlative:
tall – taller – tallest
cheap – cheaper – cheapest

- Adjectives ending in –e only add –r to form the comparative and –st to form the superlative.
nice – nicer – nicest
late – later - latest

- Adjectives ending in a vowel + a consonant, double the consonant:
big – bigger – biggest
thin – thinner – thinnest

Note: real, right, and wrong always have more and most.

2. Two-syllable adjectives
2.1
- Adjectives ending in consonant + -y have –ier and –iest:
pretty – prettier – prettiest
easy – easier – easiest

- Adjectives ending in –ow, –er, and –le normally take –er and –est, although more and most are also possible:
narrow – narrower – narrowest
clever – cleverer – cleverest
noble – nobler – noblest

2.2
- The rest use more and most to form the comparative and the superlative, respectively.
surprised – more surprised – most surprised
frightful – more frightful – most frightful

However, many two-syllable adjectives may have both forms:

polite – politer/more polite – politest/most polite
common – commoner/more common – commonest/most common

Other adjectives that may take both forms are: able, angry, friendly, cruel, gentle, handsome, pleasant, quiet, simple, sour, and obscure.

3. Three-or-more-syllable adjectives
Adjectives of three or more syllables have more and most:

interesting – more interesting – most interesting
beautiful – more beautiful – most beautiful

Nevertheless, words such as untidy (the opposites of two-syllable adjectives endingin –y) are an exception and take –er and –est:

unruly – unrulier – unruliest
uncanny – uncannier – uncanniest

Some compound adjectives have a first element consisting of an adjective which would normally form a comparative or superlative in one word,either by adding -er/-est, or by an irregular form. Such compound adjectives can therefore form a comparative/superlative by using these changes to the first adjective, rather than by using more/most. However, more and most are also possible:
good-looking – better-looking/more good-looking – best-looking/most good-looking
well-known – better-known/more well-known – best-known/most well-known

There are certain modifiers which you cannot logically be used in the comparative and superlative forms. Adjectives like “perfect”, “unique”,or “instantaneous”, for instance, express conditions that do not allow for degrees of comparison. Something cannot be more perfect than another thing: it is either perfect or not perfect.

Note: if you are not certain, you should check a dictionary to see which words use more and most and which words take the suffixes -er and -est.

Exercises:
Elementary(1º ESO y 2º ESO)

Intermediate(3º ESOy 4º ESO)

*Irregular adjectives will be treated in a different article.