Definition - Adjectives are words that describe nouns or pronouns. They may come before the word they describe (That is a cute puppy.) or they may follow the word they describe (That puppy is cute.).

Definition - Adverbs are words that modify everything but nouns and pronouns. They modify adjectives, verbs, and other adverbs. A word is an adverb if it answers how, when, or where.
The only adverbs that cause grammatical problems are those that answer the question how, so focus on these.
Examples: He speaks slowly.
Answers the question how.
He speaks very slowly.
Answers the question how slowly.

Rule 1. Generally, if a word answers the question how, it is an adverb. If it can have an -ly added to it, place it there.
Examples: She thinks slow/slowly.
She thinks how? slowly.
She is a slow/slowly thinker.
Slow does not answer how, so no -ly is attached. Slow is an adjective here.
She thinks fast/fastly.
Fast answers the question how, so it is an adverb. But fast never has an -ly attached to it.
We performed bad/badly.
Badly describes how we performed.

Rule 2. A special -ly rule applies when four of the senses - taste, smell, look, feel - are the verbs. Do not ask if these senses answer the question how to determine if -ly should be attached. Instead, ask if the sense verb is being used actively. If so, use the -ly.
Examples: Roses smell sweet/sweetly.
Do the roses actively smell with noses? No, so no -ly.
The woman looked angry/angrily.
Did the woman actively look with eyes or are we describing her appearance? We are only describing appearance, so no -ly.
The woman looked angry/angrily at the paint splotches.
Here the woman did actively look with eyes, so the -ly is added.

She feels bad/badly about the news.

She is not feeling with fingers, so no -ly.

Good vs. Well
Rule 3. The word good is an adjective, while well is an adverb.
Examples: You did a good job.
Good describes the job.

You did the job well.

Well answers how.
You smell good today.
Describes your odor, not how you smell with your nose, so follow with the adjective.
You smell well for someone with a cold.
You are actively smelling with a nose here, so follow with the adverb.

Rule 4. When referring to health, use well rather than good.
Examples: I do not feel well.

You do not look well today.
NOTE: You may use good with feel when you are not referring to health.
Example: I feel good about my decision to learn Spanish.

Rule 5. A common error in using adjectives and adverbs arises from using the wrong form for comparison. For instance, to describe one thing we would say poor, as in, "She is poor." To compare two things, we should say poorer, as in, "She is the poorer of the two women." To compare more than two things, we should say poorest, as in, "She is the poorest of them all."
Examples: One Two Three or More
sweet sweeter sweetest
bad worse worst
efficient* more efficient* most efficient*
*Usually with words of three or more syllables, don't add -er or -est. Use more or most in front of the words.

Rule 6. Never drop the -ly from an adverb when using the comparison form.
Correct: She spoke quickly.
She spoke more quickly than he did.
Incorrect: She spoke quicker than he did.
Correct: Talk quietly.
Talk more quietly.
Incorrect: Talk quieter.

Rule 7. When this, that, these, and those are followed by nouns, they are adjectives. When they appear without a noun following them, they are pronouns.
Examples: This house is for sale.
This is an adjective here.
This is for sale.
This is a pronoun here.

Rule 8. This and that are singular, whether they are being used as adjectives or as pronouns. This points to something nearby while that points to something "over there."
Examples: This dog is mine.
That dog is hers.
This is mine.
That is hers.

Rule 9. These and those are plural, whether they are being used as adjectives or as pronouns. These points to something nearby while those points to something "over there."
Examples: These babies have been smiling for a long time.
These are mine.
Those babies have been crying for hours.
Those are yours.

Rule 10. Use than to show comparison. Use then to answer the question when.
Examples: I would rather go skiing than rock climbing.
First we went skiing; then we went rock climbing.