Okay, firstly, I'll give you a small run through as to what was in Battlefield Bad Company 2, and then give an extension as to whats definitely available in Battlefield 3.
Battlefield Bad Company 2 features 2 wide-scale game modes, Rush and Conquest.
I will put this into MW2 terms for you, being as you played it.
Conquest is Domination, 3 flags, except in Battlefield you lose tickets (they're called tickets in this game) by dying as well, I think. Bottom line: Control the locations.
Rush is familiar to Demolition, if its the case that there are two bomb sites and you need to blow each one up, before the timer ends. Instead of a timer, you have, you guessed it, tickets. The case with these tickets is that it goes down by 1 per death (although if you're a medic and you revive someone, that ticket is gotten back - more on that later).
After you blew up both bomb sites, a new location in the map is opened up behind the previous 2, with simply a different setting. Tickets are restored either to 100 or 75 (if it's below 75 it goes to 75) usually, and the attackers must blow it up again.
Defenders don't have tickets, but once this has happened a certain number of times, the game ends, and the attackers win.
If you stop them, the defenders win.
You also have Squad-based team modes, which is Squad Rush, and Squad Deathmatch.
A squad is 4 people, and those four people can spawn directly behind one another because they are in a squad, with the addition of gaining additional points for helping a squad member relative to a team member. For instance:
Reviving someone = 50 points
Reviving a squad member = 80 points
Spotting Assist = 20 Points
Squad Spotting Assist = 30 Points
Kill Assist = 10 Points / 30 Points (Critical Kill Assist)
Squad Kill Assist = 20 Points / 40 Points (Critical Kill Assist)
Usually it increases by 10, as you can see.
Squad Rush is the same thing, but on much smaller scale and only with a Squad.
Squad Deathmatch is 4 squads, working against eachother to obtain 50 kills. You have yourself and three allies, fighting against 12 enemies who are also fighting eachother.
It's a 4v4v4v4, but there's a small twist - there is an Anti-Infantry Vehicle in the middle of the map, and whoever has access to that generally has a large advantage. This is kind of familiar to how picking up a weapon in Halo would work, but it's only present in this mode.
Now, more onto the core gameplay.
With the core gameplay you have 4 classes, Assault, Engineer, Medic and Recon.
Assault has an Assault Rifle which is most effective in short bursts, an Underbarrel Grenade Launcher / Underbarrel Shotgun / Underbarrel Smoke Launcher, depending on his or her choice. They also carry a sidearm (composing of several pistols, an automatic pistol and a Tracer) like every other class and their 4th Item (third being underbarrel, second being pistol, first being primary weapon) is Ammo Packs which will resupply allies (and give +10 points / +20 points each time) and yourself if you're near it.
You have an unlimited amount of Ammo Packs, but the thing is they have a cooldown timer - you can't spam 15 in quarter of a second, you need to wait a while until you can plant the next one, and when you do, the first one you planted dissipates.
As an Engineer, you carry a silenced SMG that has no real firing method, because it's simply close range (although tapping the left mouse button gives it a surprising brilliance in long-range damage). Your second item is identical to any other class, your third is a choice between 2 types of Rocket Launchers which work in conjunction with the Tracer, or a Rocket Launcher which follows where you aim, or Anti-Armor Mines.
Depending on your style, you can pick either.
Your 4th is a Repair Tool, which allows you to repair allied vehicles (or damage enemy ones) which can seriously help the longevity of your armor on the field. Like Ammo Packs, they have no limit to how much they can be used, however if you do use them for too long, they work as if they overheated - you need to wait a short while before you can use it again.
Which gives you ample time to throw a rocket at an enemy, by the way.
A Medic is familiar, except it's a very powerful support class, probably the most powerful. It's first weapon is an LMG, which becomes more accurate the longer you hold down the trigger (although Tapping does work with some of the LMG's). Your second item... do I have to say?
Your third item is choiceless - it's Defibrillators, if an ally is critically injured (Which is whenever they die when they was not in a vehicle, which can be very often), you can hit them with these two pads and they will miraculously jump back up and aid you in the fight once more.
Your fourth item is a Medical Kit, which acts just like the Ammo Pack with one exception - it heals people around it, not give them ammo.
The Recon is generally regarded a simple class, given its main weapon - the Sniper Rifle. You've some choice as to what exactly you want as a Sniper, between Single-Shot, Semi-Automatic or even Full Automatic. Your sec--.
Your third item is a choice between some very powerful C4 or a Mortar Strike activated via Aiming (and holding down the left mouse button) the Binoculars you get from it.
The C4 can only be thrown, and not a very far distance - it is very powerful however and if you feel like switching your sniper for another weapon (more on that later), it's perfectly viable (I've gotten top of the board like this).
The Mortar Strike goes vertically, meaning that if the guy is under cover, and that cover can't be blown up, then good luck with killing him using this as a weapon.
It also has unlimited ammunition - but again, a cooldown.
The fourth item is a very useful Motion Scensor.
Do you remember the Blackbird from Black Ops? The UAV that couldn't be shot down, revealing the location of all enemies and the point they are facing?
Well, Motion Scensors are little balls that can be thrown, doing the exact same thing in a radius around them. A very good radius too.
You want to know what's awesome? You get points if an enemy is killed when they were in your Motion Scensor radius, because it counts as "spotting".
I'll talk about Spotting now.
Spotting is pressing the Communication Button to tell everyone in your team where an enemy is, and is stays on the enemy for... I don't know, 10 seconds I think. It gives a precise update on where the enemy is, and on the map where they are facing.
This is a key advantage as a Sniper, usually being on the high ground and out of the danger, you can safely and very quickly communicate key positions to your allies using this function. You won't need to manually communicate the location of each enemy, if they are within close proximity to each other.
Any class can do this, although the Recon Class is generally more effective given the situations it will more often be in.
Each class also carries a single grenade, which does high-infantry low-armor damage, and is incapable of destroying walls.
This will be my first post, one moment, as I will type another
