Fastest ways to gain XP

Solution 1:

XP for killing enemies has been intentionally minimised in this game.

Quest XP is the best way to level - happily, side quests and Witcher Contracts are also a fairly good source of XP.

One thing to bear in mind is that you will get no XP for any quest more than 6 levels beneath your current level (it will turn grey in the Journal).

Solution 2:

The main quest is by far the best source of XP in the game. This is probably intentional as it makes it harder to completely overlevel for the main quest by doing all the side quests first.

Contracts and side quests can give good amounts of XP, but that varies quite a bit between individual quests.

Quests that are at least 6 levels lower than your own level don't give any XP at all (those are marked in grey). If you want to maximize XP, you should do any quests before you outlevel them that much.

Monsters give almost no XP at all compared to quests.

The game is designed in a way that encourages you to follow the main story at least some of the time. Mixing main quests and side quests is the best way to ensure that you're at roughly the same level as the quests. Just try to collect a large number of quests, do any side quests at your level and if there aren't any more of those, do a main quest or two until your level increased. Then you'll be able to do some higher-level side quests or contracts.