If you regulary played BF2 at some point, or know the mechanics well, then the manual should include all important differences (except for the presence of teamwork of course, that can't be written down in a manual) -
https://www.realitymod.com/manual/pr_manual.pdf
Now, to quickly sum up:
There's two major gamemodes, Assault and Secure and Insurgency. Other gamemodes include a co-op mode (not comparable to ArmA, mainly for practice), a strategically inspired Command and Control mode that is sadly underplayed, and a Vehicle Warfare mode without infantry, that is also not often played sadly - so I'll only explain AAS and Insurgency now.
AAS is similar to BF2's gameplay in a way. You have to capture "flags" - or more accurately, areas. The maps in AAS gamemode are usually between 2x2km and 4x4km large, with up to 1km of view distance - the smallest maps being 1x1km, which is still bigger than many BF2 maps (don't worry, no Karkand here^^)
Instead of capturing these flags randomly as the player wishes, there is a "pre-planned capture order", as the loading screen calls it. Sometimes there are two areas that you can secure at one time, often it is one. You control the area by eliminating the enemies in the area and then holding the position - then the next outpost can be captured, while the recently captured one has to be defended.
Using supply crates from helicopters or supply trucks, and the help of a squad or two, firebases (aka FOBs) can be created anywhere on the map; though their number is limited. A number of defense structures can be constructed around such a firebase, including heavy machine guns and anti-tank missile launchers, and simple things like foxholes and razor wire.
Most importantly, one can respawn at those fire bases. Unlike BF2, you can not respawn on your squad leader or captured "flags" - instead, you can only spawn in the main base, at FOBs, and at your squad's "rally point".
This rally point can be placed by your squadleader (not when he's alone!) and disappears after a minute or two. This means, it can be used to let a recently joined player jump right to the front, or, if only two men died in the last engagement, let them respawn - but if the whole squad was wiped out, they'll have to respawn elsewhere because they cannot place a rally point (obviously).
There is a number of kits you can spawn with - that is the Officer kit (for squad leaders; includes some squad-leader specific items), the Rifleman (scoped or unscoped; includes the usual stuff... A rifle, some grenades, smoke grenades, a shovel to help build firebases and alot more stuff), the Automatic Rifleman (SAW gunner), the Rifleman Specialist (got a breaching shotgun - that can also be used as a less-lethal shotgun in insurgency gamemode against civilian collaborators), and the Medic. More kits can be requested at forward outposts and the main base (at supply crates) or near vehicles (depending on the kit). Those include crewman and pilot kits, anti-tank kits, combat engineer kits, marksman kits, grenadier kits and many more.
The medic system works similar to BF2: You have a medic bag to heal people (look at them and hold left mouse button!) and epi-pens to revive people who got shot but didn't die yet (they can die if they get shot twice in a row, or if something big hit them, or if they chose to "give up" at the spawn selection screen, which speeds up their respawn time but costs the team a ticket - tickets are the number or reinforcements left, losing vehicles costs several tickets). A revived soldier will be at low health and bleeding out, so he needs treatment. Anyone who is shot, in fact, will be bleeding out slowly. Every soldier has a field dressing with gives a little boost to the health and can therefore slow down bleeding a bit, but a medic is usually still required to get the wounded back into a stable condition.
In insurgency, you do not fight over "flags" - you instead search (or defend) hidden weapon caches. You can gain intel by fighting, arresting insurgents, and arresting civilian collaborators - you lose intel by shooting those. Arrests are done with the zip-cuffs in your inventory. With enough intel, an icon will appear on the map, somewhere near a cache.
Insurgents are not equipped like regular soldiers of course. Their arsenal includes suicide cars and trucks and IEDs, so watch out as a BluFor. As OpFor, try to ambush the enemy, because you'll not have their technology and are usually stuck with an AK, some grenades, and an IED.
Hope that little insight will give you a general idea of the gameplay. The mod is free, so feel free to hop into a game
(Remember to patch your BF2 to 1.5 - you need patch 1.41 before that - if you didn't already).
The current download page only has the links for the next version which'll be out at friday, but someone surely can give you the old download links if you want to try it out before friday.
Welcome to the forums! Make sure you have a working mic, read the manual, and at some point, you might want to take a look into the often used third party voip program "mumble" that allows you to have positional audio effects to talk to non-squadmembers like pilots and crewman of the chopper/APC you are in, or friendly squads near you.