It's 4 player co-op versus 10 waves of enemies with objectives to complete during waves 3, 6, and 10. Then there is a final extraction wave where you hold out for 2 minutes before your shuttle comes to pick you up. Completing missions gets you XP to level up and credits to buy 'packs' in the store. You can also buy packs with real $ but it's not necessary at all; I've never spent a dime on multiplayer. The multiplayer dlc is free, but not the campaign dlc.
There are four difficulty levels, bronze, silver, gold, platinum with a nice progression. You could hop into bronze and within a few games be contributing. Each level of difficulty is roughly twice as hard with twice the reward. There is a shit ton of weapons and characters to choose from, too many to list. You rank up your powers with skill points you earn from gaining character levels. Max level is 20 and it doesn't take long to get there. Each character as 5 powers. We'll call them powers 1 through 5. Power 4 is always passive bonuses to weapon damage, power damage, and weight capacity. Power 5 is always bonus to health and shields or melee. Powers 1 to 3 form a unique set of abilities for each character. No two characters have the same combination of powers 1 to 3, which is what makes them all so unique.
It's in over the shoulder shooter much like Uncharted. The only time you go into first person is when firing a sniper rifle. It's amazing fun; the most fun multiplayer game I've ever played, hands down, no contest. You can't even see Destiny in the rear-view mirror. Maybe, on the distant horizon, you can Bad Company 2 somewhere back there, but this game is definitely way out in front on my list of multiplayer favorites.
There is no need whatsoever to play the campaigns first. Lepercolony has played 700 hours of multiplayer and still doesn't know dick about the story.