This is the infamous airport level. There is an actual battle at the end, so I'll give you a quick cover on that. Regardless, let's start at the beginning. Step out of the elevator and get into position. Now, you don't actually have to kill anyone. In fact, Makarov and his men will normally take out everyone before you anyway. It's hard to get ahead of them, since you apparently can't run in an airport.
After the initial slaughter, move on up the stairs with the team and take out the food court. Curve over to the space by the elevator. You can engage the security team here, or just wait for some explosions to take them out. Move forward and around to the gate. You should be able to move up to a little jog as you move out of the airport. Check your ammo and walk outside to begin the real battle.

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There's a real security response now, and we have to fight our way out of it. Use the grenade launcher to blow away the first group of police with riot shields. You can also rake machine gun fire across them to wound them. Then you just have to get a few more shots in while they have the shielded lowered.
Advance down the tarmac under the airplane. Take cover behind the center post and use your machine gun to clear out the police in the top level of windows. There are more riot shield carriers moving toward you, so either repeat the gun trick or use some grenades and flashbangs to take them out. Be very careful when moving up to the next area though. There's a spawn point on the burning van to the left and the security building to the right. It's very easy to walk into an ambush here.
Get behind a pillar and help Makarov clear out the police line ahead of you. There should be about 6 officers at the end. Just pick them off or blow them up. Advance a bit more with Makarov and mop up any stragglers. Then follow him into the garage area. Get into the ambulance to trigger the ending cutscene.