I'll go first, being the thread author and all. The single shooter I've played most is TF2, so I'll explain Brink to an audience that is familiar with TF2.
Beginning with the broadest qualities of the game, Brink is a fundamentally teamplay-based shooter. Where TF2 has nine classes, each of which has unlockable customisation items, Brink has four classes, three body types, and many, many guns. The biggest difference between Brink and TF2 is that your class only determines part of how you play: it decides what special tools you have for interacting with your team, but not what guns you can carry. Every class is equally good at shooting people, which means you should never be guilted or trapped into playing Medic or Engineer just because nobody else will. It also means every class has useful ways to interact with teammates on the battlefield, so Medic and Engineer aren't on a special pedestal. Soldiers provide ammo to teammates (and this ammo can contain buffs, depending on the Soldier's specialisation), Operatives hack into fallen enemies' comm systems and reveal the locations of enemy combatants on your radar, Engineers (in addition to building sentry guns) place mines and buff their allies' guns to do more damage, and Medics (in addition to simply healing allies) can buff allies' maximum health and toss adrenaline syringes to downed allies who haven't been completely finished off (and haven't respawned) yet. Basically, your class determines what you can do when you're not shooting someone.
Like TF2, and unlike most other shooters, Brink gives you a tradeoff between health and mobility. The three different body types are basically a sliding scale between "cool guns" and "cool moves"; if you play as a skinny guy, your quick gait and wall-climbing skills give you access to paths other types don't, like the Scout has in TF2. If you play as a beefy guy, you can carry big machine guns, like the Heavy, and you don't even have to be fat and bald. And, of course, there's the middle ground: you can carry decent guns and still be able to climb some walls if you play as the mesomorphic Medium.
Weapon damage adheres to a philosophy that should be familiar to TF2 players: killing anyone instantly takes some finesse. In fact, Brink goes so far as to eliminate the concept of snipers by making even the slowest, scopiest, most bolt-action guns unable to kill a healthy enemy with a headshot, and by being set in an environment where it's rare to have a line of fire long enough that the enemy can't shoot you back without a scoped weapon.
Weapon accuracy is a bit more like TF2 than other shooters tend to be; your accuracy doesn't completely disappear while you're moving. Brink's developers like to run and gun, and they're going to make this viable. However, you will be able to aim down your weapon's sights to improve your accuracy (at the expense of your movement speed). Weapons can be customised in a variety of ways; if you want to run and gun, you can attach a foregrip to improve your aim while you're on the move, and if you prefer to crouch and aim, you can attach a dot sight or a scope.
Brink is as objective-focused as TF2, which is to say, more so than other shooters. Dying just means you have to respawn; it doesn't get the enemy closer to victory, so there's seldom a reason to simply take cover and hide. Brink maps are most anologous to TF2 Attack/Defend maps, in that once your team completes a primary objective, the other team can't un-complete it. The same sort of clock scheme is in Brink as in TF2: you have a limited amount of time to complete the first objective, but if you do it, you get plenty more time to complete the next objective. The difference is that the objectives themselves are class-based: instead of simply occupying an area for a time, your team has to get a member of a certain class there in order to use its class tools. This results in three different types of objective:
- Engineers stand at the Construct/Repair objectives and use their repair tool (so teammates need to secure the surrounding area to keep you alive),
- Soldiers have to plant a charge at Destroy objectives and make sure enemy Engineers don't disarm it (so, once the charge is planted, the enemy has to actually move to the objective to defend it, instead of just shooting you),
- and Operatives are able to use their wireless hacking tool to complete Hacking objectives from a short distance away once they've applied a transponder to the target (but hacking is faster if the distance is smaller).
There's also a variety of other objectives. Command Posts are like TF2 control points, in that they can be captured and recaptured many times. They're never the primary objective, but they are very useful in that, as long as you own one, you can use it to change class, change weapons, and refill ammo, and it gives every member of your team a buff.
Brink uses a common shooter element that is absent from TF2: experience point progression. You gain XP by using your class tools to complete objectives or help allies, and by killing enemies (kills that are made close to an objective are more valuable). You use XP to unlock specialisations for your character. Splash Damage doesn't commit the infuriating sin of forcing you to unlock essential class tools: a Medic can always heal, a Soldier can always crap ammo, etc. However, with specialisations you get through XP, you earn the opportunity to give up some of your class tools (e.g. the ability to buff a teammate's max health) for others (e.g. a special grenade that can revive several teammates at once). Brink skills are much like TF2 items, except you actually get to pick which ones you earn. (You will never have to deal with finding the Force-a-Nature six times before you get your first Kritzkrieg.)
There are other forms of character customisation. Unlike TF2, the classes don't fight in completely different ways, so Splash Damage doesn't do what Valve did and make each class have its own distinctive look. Instead, you craft your character's look using clothing, body armor, and helmets that you unlock through gameplay. This area of customisation doesn't affect gameplay at all; you can go shirtless if you want, and your chest will absorb just as many bullets as the guy with the bomb squad suit.
Brink has bots. We're told the bots are really good, and if the bots from Splash Damage's previous game, Enemy Territory: Quake Wars, are any indication, we're not being deceived. Players who are intimidated by online multiplayer can play the same game against bots to build their skills. You still earn XP when you're playing against bots, and this also means you can set up a private match and play cooperatively with a friend.
Finally, Splash Damage is trying its hardest to make Brink a game that builds a competent player base. You shouldn't ever have to worry about your team's newbies not understanding their class skills ("this team has three engineers and no teleporters!" "i burned to death and a pyro who could have extinguished me was right there!"), because Brink actually tells its players that these are objectives. Brink has a feature called the Objective Wheel, which is an interface where players can see everything they can do to earn experience at whatever moment they look at it. If you're wounded, and a nearby Medic checks his objective wheel, he'll be told he can make some easy XP by healing you. If you're getting low on ammo, the Soldier's objective wheel tells him to toss you some. Naturally, the primary and secondary map objectives are on here, too: a huge arc at the top of the Objective Wheel is taken up by whatever the primary objective is, at all times. You are never required to use the Objective Wheel in order to perform objectives, but if you do, your character announces to your team that you're going to perform the objective you've selected, which lets smart teammates know what you're planning and allows them to help or get out of the way as appropriate.
If you love TF2, I think you'll love Brink, because Splash Damage, like Valve, thinks long and hard about how the game should work to make it fun, and isn't afraid to break with convention where it will improve the game. Get Brink for PC and play it with me. I will buff your gun.