1. I. Comparatives come in three varieties:
Superiority más... (que)
more... than or ____er than
Inferiority menos... (que) less/fewer... than
Equality tan... como as... as
tanto... como as much/many as

2. más inteligente (more intelligent) más cariñoso (more loving)
In English, to create a comparison with an adjective, we generally add an "-er" to short adjectives (happier, stronger, wilder, etc.) or add the word "more" before longer adjectives (more intelligent, more studious, more loving, etc.). There's no Spanish equivalent for the suffix "-er"; we simply precede all adjectives with the word más (more) to make them stronger.
más fuerte (stronger)
más rádido (faster)
más inteligente (more intelligent)
más cariñoso (more loving)

3. To indicate "less" rather than "more", we precede all adjectives with the word menos to make them weaker.
menos fuerte (less strong / weaker)
menos rápido (less fast / slower)
menos inteligente (less intelligent)
menos cariñoso (less loving)

4. Comparisons of Inequality with Adjectives
In order to actually compare two objects in a comparison of inequality (one object being more or less ____ than the other), we use the following construction:
subject + linking verb + más/menos + adjective + que + noun
Marcos + es + más + alto + que + su hermana.
(Marcos is taller than his sister.)
Yo + soy + menos + inteligente + que + tú.
(I am less intelligent than you.)
Mi coche + es + más + rápido + que + el tuyo.
(My car is faster than yours.)
La puerta es más roja que una cereza.
(The door is redder than a cherry.)

5. Comparisons of Equality with Adjectives
While a comparison of inequality compares two objects or people with different characteristics, a comparison of equality means that the two objects have equal characteristics.
In order to make these comparisons, we use the adjective with the expression "tan ... como...", which is like saying "as ... as... ". See the construction below:
subject + linking verb + tan + adjective + como + noun
Marcos + es + tan + alto + como + su hermana.
(Marcos is as tall as his sister).
Yo + soy + tan + inteligente + como + tú.
(I am as intelligent as you.)
Mi coche + es + tan + rápido + como + el tuyo.
(My car is as fast as yours.)
La puerta + es + tan + roja + como + una cereza.
(The door is as red as a cherry.)

6. Comparisons with Superlatives
Superlatives are also used in comparisons. In English, we create superlatives by placing a definite article before the adjective, to which we add the suffix "-est" (the strongest, the smartest, the nicest, etc.). To turn this into a comparison, we add the group to which the object or person is being compared (She's the prettiest in the class / at the party / of her friends.).
To convey this same concept in Spanish, we use a construction very similar to the other comparison formulas we have reviewed, with the definite article (el, la, los, las) preceding the comparison word (más, menos) and using de instead of que.
subject + verb + definite article + más/menos + adjective + de + rest of sentence
María + es + la + más + guapa + de + sus amigas.
(María is the prettiest of her friends.)
Mi coche es el más caro de todos.
(My car is the most expensive of them all.)
Sara es la menos alta de su clase.
(Sara is the least tall of her class.)
Pedro es el menos rápido de su equipo.
(Pedro is the least fast of his team.)

7. Comparisons with Adverbs
The same formula is used in comparisons with adverbs, the only difference being that you won't have to worry about gender given that adverbs have only one form. (Need a refresher on how to form the superlative? Take a look at this page: Spanish adverbs)
subject + verb + más/menos + adverb + que + noun
Sara + estudia + menos + diligentemente + que + Marcos.
(Sara studies less diligently than Marcos.)
Su casa + está + más + lejos + que + la mía.
(His/Her house is farther than mine.)

8. Irregular Comparisons
Both English and Spanish have several "irregular" comparison words, meaning that the adjective changes. Take, for example, the adjective "bad". If we followed normal rules for forming comparisons, we would say "badder" instead of the irregular comparison word "worse". The same goes for Spanish; the word for bad is "malo" but in comparisons instead of saying "más malo" we say "peor".
See a few examples below:
Normal adjective Adjective in comparison
good = bueno better = mejor
bad = malo worse = peor
big = grande bigger = mayor (referring to age)
old = viejo older = mayor
young = joven younger = menor
little = pequeño littler = menor (referring to age)

9. Examples in context:
I'm older than my sister. = Yo soy mayor que mi hermana.
My sister is younger than me. = Mi hermana es menor que yo.
Your grades are worse than mine. = Tus notas son peores que las mias.
I drive better than my father. = Conduzco mejor que mi padre.

10. To form comparisons of equality with nouns, use the following formula:
tanto(-a,-os,-as) + noun + como
Juan tiene tanto dinero como María.
(as much money as)
Él tiene tanta paciencia como ella.
(as much patience as)
Tiene tantos libros como ella.
(as many books as)
Tiene tantas plumas como ella.
(as many pens as)

11. To form the comparisons of equality using adjectives or adverbs, use the following formula:
tan + adjective (adverb) + como
El libro es tan bueno como la película.
(The book is as good as the movie.)
El chico es tan alto como la chica.
(The boy is as tall as the girl.)

12. When actions (not things) are being compared, and there is no adjective, use the following formula: verb + tanto + como Sus estudiantes aprenden tanto como mis estudiantes. (learn as much as) Rosario cocina tanto como Josefina. (cooks as much as) Las naranjas cuestan tanto como las manzanas. (cost as much as)

13. When actions (not things) are being compared, and there is an adjective, use the following formula: verb + tan + adjective (masculine form) + como Aquí se trabaja tan duro como ahí. (work as hard as) El niño juega tan poco como la niña. (plays as little as) Ellos duermen tan poco como ella. (sleep as little as)