In a close firefight, if you're hit, don't immediately go for your bandage. If the enemy is smart, they'll be coming around the corner very soon, especially if your numbers are few. If you're smart and you know you hit someone, expect them to be bandaging themselves, or else not be expecting you to come around the corner (still applies even if you yourself were injured).
If you've just finished a firefight with the enemy and a few of your guys are down, help the medics by bandaging people they have yet to get to. It will save the medics bandages, and speeds up the process of getting the squad back up.
Spread out. Ten to fifteen meters should be between you and all of your squad mates, otherwise there's a great deal of your squad that's within the blast radius of just a single grenade or other explosive device. Spreading out also keeps you safe from getting gunned down one by one with ease as you enter buildings or move into any open area.
When a firefight starts, return fire. Be mindful of which colour your friendlies' tracers are, and fire in the direction of the enemies' tracers, muzzle flashes, and movement. If you don't know where they are, then guess. You have a better chance of surviving a firefight when you lay down suppressive fire than when you rely on luck not to get shot.
In a long range firefight, as soon as your squad pinpoints the position of the enemy with whom you are engaged, the grenadier needs to mark their position with smoke, and then both the grenadier and whoever has the RPG/LAW needs to be using it. I can say, without a doubt, that in a long range firefight the biggest killers are the ACOG sights and explosives.
Medics should never pile up if it can be avoided.
Save your stamina. If you're about to enter an urban area full of enemies, you want to have stamina in case you need to haul ass across a doorway to flank.
In much of the same way, you want to use your stamina getting across places where you're much easier to be seen, like fields.
If you and your squad saw some enemies in a field and opened up on them, but only managed to pin them down, open up on them with the explosives. Do not run out into the field they occupy. If you don't have explosives, circle around to the sides of the field and peek over the walls that enclose it.
If you are that guy who gets pinned in a field, get out of there ASAP. Don't sit in the same place the enemy just watched you drop in, but instead move, bandage up, and crawl to an opening in the enclosed wall.
This one might seem oddly specific, because it is, but if your squad mate just found an enemy FOB and is calling for assistance to dig it up, haul ass. If it's in an enclosed area, like a building inside a compound, just get inside that building as soon as you can and dig it up. Don't take your time, and don't get lost trying to find them. Just check your map and move.
