Grammar: Bad vs. Badly

Bad is an adjective that modifies nouns and pronouns.
Badly is an adverb modifying verbs, adjectives and other adverbs.

If we review linking verbs and subject complements, we will have a better understanding.

A linking verb links or connects a subject and its complement.
A subject complement renames or describers the subject.

Example: The test was difficult.

A partial list of linking verbs may include:

• The forms of be
• Verbs associated with the five senses: taste, feel, sound, smell and look
• Appear, seem, stay, prove, remain

Some of these words may or may not be linking verbs, depending on how it is used in the sentence. When in doubt, look at the sentence and use the following notes:

• Note #1 If the word that comes after the verb modifies the subject, the verb is linking and the word should be an adjective.
  
• Note#2  If the word that comes after the verb modifies the verb, the word should be an adverb.

Now lets go over note #1, and use bad as an example.
When you describe yourself, it is correct to say:
I feel bad.

Why is this correct? Let's apply #1:
The subject is I.
The verb is feel.
The word that comes after the verb is bad.
Bad modifies the subject.
Bad is used instead of badly because bad is an adjective.

Question: So what about this sentence?
I feel badly.

This means something altogether different.
Why?
Badly is an adverb.
Adverbs describe verbs and other adverbs.
In this sentence, badly is describing the verb, feel.

The sentence implies that something is wrong with the physical sense of touch.