Unfourtunately there is little information out right now. Later as the game progresses we might be able to get more information. However this is what I managed to scrape up:
From this information site:
Get More Supply Drops
About the 3 Types of Supply Drops
- Weapon Loot (custom weapon variants)
- Character Gear (changes your appearance; doesn't affect gameplay)
- Reinforcements (single-use bonuses)
This one comes with a disclaimer: It's very likely a glitch that Sledgehammer Games will get around to fixing. But use it now while you still can, and you'll score some sweet gear.
YouTuber Quadmft discovered that in multiplayer levels, if you die when you first enter, it gives you a Supply Drop. He says it works every time, but this is the important part: don't kill another player before you die. Enter the level, let someone kill you, and respawn. You'll immediately get a fresh Supply Drop.
- Gold: kill 50 enemy players while using no weapon attachments
- Diamond: complete every camo challenge for the weapon in question
- Royal: complete every camo challenge for all the weapons in this class
Read more: http://www.techtimes.com/articles/19537/20141106/call-duty-advanced-warfare-rank-up-fast-best-camos-more.htm#ixzz3KgrjzlCn