Common items may drop after every match played in offline and online until they are all unlocked. It doesn't matter if the match is won or lost, it's a random chance given by the server the match is played at.
Uncommon items, Rare items, Very Rare items, Painted items and Certified items may drop randomly after playing online matches. This drops occur only during the first 10 hours of playtime each week. The week resets on Thursday, Friday or Saturday - the exact moment depends on a player's timezone.
Import and Exotic items may only be obtained by combining five items of the same quality starting at the Very Rare Rocket Boost and Player Banner. This items don't drop after playing online matches and are still Painted.
By opening Crates. Crates may drop randomly after playing online matches and do not count against the normal item drop limit. They are a completely separate system, and require purchased keys to open them.
By combining five items of the same rarity in the 'Manage Inventory' screen to obtain higher rarity items within the same set. This can be used to obtain Very Rare items, and those can be used to get an item of higher quality.