How do item drops work?

If you mean from online matches, you can get Uncommon, Rare, Very Rare, Painted and Certified items as a random drop after a match.

The only rule I know is that these drops only occur during the first 10 hours of playtime each week, after that you will no longer receive item drops.

EDIT:
After the 2018 Summer Update the system of levels, exp points and drop has dramatically changed, now you always get an item drop every level up, which occurs every 20.000 xp points you earn. The item can always been Certified and/or Painted, and only from the same limited item pool, this means you can never obtain an item which is already present in a crate.
Crates, instead, continue to drop randomly as before.

(Source: Rocket League wikia)