Choose Random Enemy and Location
I usually create a new match rather than finding one because I often find that I get a horrendous connection if I just search. I have played with people in Russia or other eastern European country before, and the amount of teleporting around and no weapon damage is frustrating. Anyway, if you choose random enemy you get a 15% experience bonus and random location gives a 10% increase. Overall that is a 26.5% increase, which is quite significant if you are doing a silver challenge.
If you galaxy readiness rating is at 100% you also get a 5% experience bonus.
Kill Enemies in Different Ways
There are bonuses for killing enemies in particular ways. There is a bonus for number of kills (Gold 75, silver 50 bronze 25), number of biotic kills (Gold 50, silver 25 bronze 10), assists (Gold 50, silver 25 bronze 10), number of weapon kills (usually called pistol, shotgun etc, if you are using 2 weapons you can get a bonus for both) (Gold 50, silver 25 bronze 10) melee kills (Gold 25, silver 10 bronze 5), and grab kills (not sure how many for the different numbers, but I think bronze 1, silver 2 and gold 5 or somewhere near that).
Each of the bonuses offer different amounts of experience rewards. Often time they are around 500 xp for bronze, 1 000 xp for silver and 1 500 for gold.
There are a few awards for team combat related stuff. If you complete 3 waves without a single team member going down you get 2 500 points, 5 000 for 5 and 10 000 for completing the whole challenge without anybody dying.
You can get kill streaks as well. I haven’t figured out how the system works, it might depend on how many points are earned rapidly, how many enemies were killed in a blow or how much damage was dealt at once. Usually you get kill streaks if you fire a rocket in a large group of enemies that contain strong enemies. I have achieved one with a nova before though.
You also get a reward for completing a challenge depending on what challenge it was (bronze, silver or gold).