Problem is often your objectives require you to be going a direction that you wouldn't need to be, so this is not the panacea it sounds like. Look natural. Duck out when it seems nobody's paying attention to you.
Dressed like an enemy, you can now go through enemy locked doors. A useful example on the fueldump map is using this trick to lead an engineer into the enemy base while everyone else is still worried about the bridge.
Note that you don't get a helmet as a covert ops guy, so you're at a disadvantage when the bullets start flying. You need to keep from being shot. When you're in the other team's uniform, your excited teammates are liable to shoot at you before they see the slash come up. The release version makes the slash easier to see, and you'll still get hosed. Itchy fingers...
As a Covert Ops guy, you'll collect class experience for marking mines, using your satchel charges to good effect, stealing uniforms, and making kills with scoped weapons. In the release version, head shots are instant kills, which makes the Covert Ops a very deadly sniper.
What does all this mean? If you're carrying around a Sten or an FG42 and spending most of your time shooting at people, you probably meant to play another class-- you don't have a helmet, so you're more likely to die, and you're not collecting covert ops experience for advancement as a covert operative. Yeah, "covert ops" sounds cool, but you're just getting yourself dead.
So what about your stuff?
1) Key 1 is your knife, and it's the most silent weapon you have. Remember, a stab in the back is an instant kill, so if you've got the sneak-fu, use it.
2) Pistol. You're the only guy who carries a silenced pistol, but remember it will take three head shots with it to bring down an uninjured enemy. On the other hand, should you ever need to be in your own uniform, you can remove the silencer and fire a shot.
3) Two-handed weapon. There are three options here; the Sten, which is a fairly fast firing (though underpowered) silenced submachinegun. The FG42 is the old "Paratrooper Rifle" from the single-player campaign of RTCW. It's not silenced, so shooting it puts you back in your own uniform, it's also slow and only holds 20 rounds per magazine. Third is the K43 or M1 Garand, depending on your team, it's silenced and is an excellent sniper weapon.
The Sten is a reasonable submachine gun for when you're working with other people, but each bullet does less damage than the Thompson or MP40 and it overheats. You can usually use it to hunt down a bad guy to steal his uniform.
I find the FG42 to be almost useless. Any time you go toe-to-toe with someone (where you're at a disadvantage due to lack of helmet), the Sten is probably a better weapon. While the FG42 is scoped, the scope has no zoom and the weapon does less damage than a Garand or K43. It also does less damage per bullet than the Thompson or MP40.
The Garand, I think, is the nicest of the bunch. Both the sniper rifles have the problem that you can't reload them until they're completely out of ammo, but you'll do so automatically if you switch away from the scope. The Garand only holds 8 rounds but makes a nice "ping!" noise when it's out of ammo; the K43 holds 10 but you'll have to pay more attention to your ammo total.
4) Grenades. You get two, and they're used like they would be in anything else, but be warned: They're noisy, so you lose your enemy uniform for using them.
5) Smoke grenades. You're usually going to be working alone as covert ops, but there comes time when it's time to make the all-hands assault and here's where your smoke grenades come in. You can cover your troops advance or your engineers laying mines from enemies seeing them to get good shot at them. Rarely is the smoke grenae useful when you're working alone-- a cloud of smoke is pretty darned visible.
6) Satchel charges. For the things you can blow up, you're a better demolitions guy than an engineer. You can destroy command posts, base fortifications, and machine gun nests quicker than an engineer can get the dynamite set. On the other hand, you now have to go find a new enemy uniform.
b) Binoculars. If you hit B quickly, a mine logo will show up-- you know there's mines if you see it. If you don't, there were no mines in the binoculars' field of view. If there were, hold B and you'll mark the mines on the command map.
Once you've collected 20 covert ops XP (note that your XP total on the screen is combined XP) you become a level 1 Covert Ops guy, and if you're not already a PFC, you become one. You can gain up to four levels in Covert ops, and you get a specific bonus with each level: