How do I get XP?
You'll get XP for most things you do around Seoul- killing enemies, completing missions, and resolving tasks around the city. You don't get it for completing contracts, Global Conflict investigations, or Wreckroom simulations.
How Do I Get *More* XP?
There aren't very many XP bonuses built into Agents of Mayhem, and not everyone will find each method to their taste, but they're all listed below.
The first is to include Braddock in your squad, and invest in her team upgrade. This can grant up to 10% bonus XP to all squadmates. There's no real downside to this, as Braddock is an excellent anchor character, but once she reaches level 20, you're technically losing overall XP on the deal.
The second is to up the difficulty- the higher you set it when deploying your team, to more XP you gain. The obvious downside is that the game becomes harder. If you're running your A-team, or focussing on minor missions this might not be much of an issue, but it certainly is possible for even a strong team to get blindsided by an over-powerful boss. In general, it's easier and quicker to run 10 missions on a normal difficulty than 6 on a much higher one.
The third way involves levelling the Agency. Any agents with a personal level lower than your Agency Level get bonus XP. So if you want to maximize your XP gain overall, one strategy is to focus on levelling a few core characters then coming back later and leveling the rest once your Agency level has soared. This has the added benefit that you can mix in high-level characters to guide low-level ones through the higher difficulty / higher XP missions.
The final and best way to up your XP gain is by purchasing the 'Gonepro Combat Diary Camera' as an Agency Upgrade once you reach Agency Level 10. Works in all circumstances, for all teammates.