I found myself needing the sniper more and more as I get into Mass Effect, taking out targets from fairly far ranges. How can I reduce my sway when zoomed in, and efficiently take out my targets with less shots? I find waiting for the cooldown can even give enough time for my enemy to get close
Sniping can be difficult at lower levels, especially if you haven't progressed far enough to have come across decent rifles. Additionally, if you haven't chosen a class with the sniper rifle talent (Soldier or Infiltrator), I'd probably just choose a different offensive strategy.
Keep in mind that even if you can't snipe, Garrus can if you equip him appropriately, and he gets an additional accuracy and sniper rifle damage bonuses from points invested in Turian Agent. Of course, relying on your squad members exclusively will almost always get you into trouble, so assuming you can properly wield a sniper rifle, there are a few things you should consider.
First, rifle choice is key. Like with virtually all weapon classes your best choice is Spectre Gear, but there are alternatives when that isn't available. If you find yourself picking up level IV weapons, I recommend trying to find a Striker (Devlon Industries). If you find yourself picking up level VII weapons, look for a Punisher (Armax Arsenal). If you're at an earlier stage, look for an Equalizer (Haliat Armory).
Once you have a decent rifle, investing points into the sniper rifle talent goes a long way. After you get to a certain level, with the right rifle there will be virtually no sway when aiming down the scope. For earlier on though, tactical use of Assassination can be helpful – just keep in mind that it has a 45 second cooldown.
After weapon choice and talent assignment, you should consider adding both ammo and weapon upgrades to your sniper rifle. Most of the sniper rifles at minimum do nearly enough damage to kill, so be sure to pick ammo upgrades that will maximize damage against the types of targets you're going up against.
For instance, Anti-personnel/Shredder (for organics) and Armor-piercing/Tungsten (for synthetics) are typically reasonable options, although once accuracy has improved enough I prefer Sledgehammer rounds. You can also give Chemical/Polonium rounds a shot, with the hope that the target will die from toxic damage before they're close enough to return fire.
When it comes to weapon upgrades, I find the heat absorption and stability modifications work well for me. These come in the form of Heat Sink/Frictionless Materials and Recoil Damper/Kinetic Stabilizer/Kinetic Coil, respectively. Depending on your needs and number of upgrade slots, Combat Optics aren't a bad choice either when they become available, since you get the detection level bonus and an increase in accuracy.
Beyond that, there are a few more minor things to consider: