Well-organised teams playing private matches can make their lives much easier by picking out a defensible area of the map and gravitating towards it on any non-objective-based waves. Having a fallback position enables you to create choke points in which the oncoming enemy get trapped in your crossfire. If you play as a character who likes to operate from distance - say an Infiltrator with a sniper rifle - it's well worth learning which locations on the map afford you the best view of the terrain, ideally encompassing multiple enemy spawn routes.
Once in place (let's not call it camping), remember to stay stuck to cover, as your shots will do greater damage. Ditto using the left shoulder button to aim. You should never be firing without zooming in. Oh, and on the subject of Infiltrators, the Tactical Cloak power is incredibly handy. It has a massive damage modifier when you fire while cloaked, so whether using a sniper rifle or roaming around with a shotty make sure you've got it switched on. And it's equally handy defensively. You can resurrect teammates or access objective terminals while cloaked without fear of molestation. Tactical Cloak is also crazy handy if you need to beat a Benny Hill-style exit from a bad spot. Speaking of which...
Keep On Movin'
The AI in aggressive, and it can be easy to find yourself overwhelmed. In which case, don't stick around to bravely duke it out. You'll only get toasted. As soon as you sense things are going trombone-shaped, leg it until you're out of trouble (the maps are all big enough to be able to find somewhere quiet enough to recharge your shields). Like most multiplayer shooters, constantly moving makes you a much harder target to pin down.
Use spectator mode to watch an expert player finish off a round once you've had a mishap, and you'll notice how they constantly do circuits around the map, using their powers rhythmically to keep the pressure on the enemy as they pick them off one by one. In fact, getting used to the exact recharge time of your character is a key skill - to harvest maximum XP you always want to be squeezing off a power as soon as you're charged.
Note also that many powers will home in on targets, even dog-legging around corners, enabling you to winkle enemies out of cover. Some can also be used in combination - such as warp/shockwave - to trigger powerful biotic explosions. The most mobile characters on the map are Vanguards, who can use their Biotic Charge move to turn themselves into human(oid) missiles, even whizzing to different levels of elevation so long as you have line of sight to the target. The level six version of the power enables you to opt for recharged barriers after a successful Biotic Charge, making it incredibly powerful - just be sure your shotgun is loaded at all times to finish off staggered enemies.
Know Your Enemy
Unless you're happy spaffing Cobra missiles, you need to learn the weakspots of the trickier, bullet sponge enemies that populate the later waves. Banshees are particularly irksome - teleporting around the map and capable of one-hit killing you (with no MediGel comeback) at close range. Strip their barriers and shoot them in the face. By contrast, the hulking Brutes don't like it in the ass. Dodge their stampede, then unload into their unarmoured spines/backsides.
Geth Pyro's are upsettingly dangerous at close range, and their flamethrowers will catch you even if cloaked, so target the fuel tanks on their back. One thing not to shoot: Your teammates. It won't hurt their health, but it will have an impact on their accuracy - and make you seem like a clown at his first rodeo. (Also, note to Vanguards: sweet though the Biotic Charge move undoubtedly is, some players will object to you jumping in constantly to 'steal' their kills. Enjoy charging responsibly if you want to make new friends.)