In Mass Effect 3 for the PC, PS3, and Xbox 360, unlocking characters to use in multiplayer is all based on a CCG system (collectible card game) where you play to earn coins (or pay real money to get them quicker), and use those coins to buy card packs with different levels of rarity of cards.
Recruit Packs (5,000 Coins)
These are the basic entry level packs that contain mostly common and uncommon cards. Supposedly you can get rares and ultra-rares from this pack, but only after you’ve exhausted all of the common and uncommon cards first, so I wouldn’t suggest using that method to get all of the cards you want. Contains specific cards not in the other packs, being Rank 1 Ammo, Armor, and Weapon bonus items.
Veteran Packs (20,000 Coins)
These mid-level packs contain common, uncommon, and a chance at rare cards. Contains specific cards not in the other packs, being Rank 2 Ammo, Armor, and Weapon bonus items.
Spectre  Packs (60,000 Coins)
The most expensive packs you can buy, the Spectre pack contains common, uncommon, and a chance at both rare and ultra-rare cards. Contains specific cards not in the other packs, being Rank 3 Ammo, Armor, and Weapon bonus items.
Which Packs to Buy?
Obviously you’ll want to start off with the recruit packs to build up some of the basic equipment, ammo, etc. If you have some money to spend, a lot of people use money to purchase a few Spectre Packs at the beginning to give them a slight edge at the start.
After that, there is some debate as to which is better between Veteran and Spectre packs. Some claim that you get better chances for rare cards in a Veteran pack since they’re one third cheaper. I think the jury is out on that one though.
Personally, I would stick with Recruit and Veteran packs for a while until you can finish Silver and Gold matches regularly. There are some pretty decent characters in the Uncommon group after all, like the Quarian Infiltrator.
Unlockable Characters from Card Packs
Here are the characters you can unlock, and what rarity group they’re in.
Common Characters
Human Characters (Appearance Mods)
Uncommon Characters
Asari Vanguard
Drell Adept
Quarian Infiltrator
Salarian Engineer
Turian Sentinel
Turian Soldier
Rare Characters
Asari Adept
Drell Vanguard
Krogan Sentinel
Krogan Soldier
Quarian Engineer
Salarian Infiltrator