Basically, when applied to language and grammar, a descriptive approach is to go out into the population and observe how people actually use the language. No judgments, good or bad, are made about what is observed. This information is analyzed, categorized and presented as a picture off how things are.
A prescriptive approach starts with rules and standards for language use.
Once these rules and standards are developed, a prescriptive approach is to present those rules as how language should be used. In this structure there are good and bad uses of language.
Take the sentence: Me and Johnny is going to the park.
A descriptivist would catalog this usage and document that this sentence was actually used by someone.
A prescriptivist would correct this usage, by pointing out:
1. An objective pronoun was used where a nominative pronoun should have been used.
2. The speaker was impolite by placing himself first instead of second.
3. A singular verb was used with a compound (plural) subject.
The result would be a correction: "Johnny and I are going to the park."