Fairly is generally a modifier of adjectives and adverbs. It suggests a limited degree.
- How was your trip? Fairly good. Not the best I’ve ever had.
- I play tennis fairly well. I will score a few points.
Quite, especially in UK english, suggests a higher degree than fairly.
- How was your trip? Quite good, you should go.
- I play tennis quite well. I might beat you.
- She studied in London, so she speaks English quite well.
Quite also modifies nouns and verbs.
- I quite like the rain.
- Paying at the bank was quite an ordeal.
3. Rather (perhaps a little old-fashioned)
Rather is a little stronger than quite. It communicates ideas of more than is normal, more than expected.
- How was your trip? Rather good. I didn’t think it would be.
- I rather like this cake. I don’t usually like cakes.
Pretty is informal and modifies adverbs and adjectives.
- How are you? Pretty well thanks, and you?
- I think this film is pretty slow.