XCOM: The First Turn

You've just landed six X-Com soldiers on an unknown patch of land deep in the Black Forest, stepped away from your Skyranger, and can't mark out where the downed Muton UFO is. Your first-turn placement can be the difference between victory and a total loss of the six dudes in a dropship standing between aliens and the annihilation of the human species.
Here are the steps that I take at the beginning of every single-player match:

The first task you have at hand is identifying the battlefield. Drag your mouse around. Zoom out. Locate the thin red lines resembling lasers -- this is the edge of the battlefield. Your sky ranger and deployment zone are a "safe" zone, and crashed objects are usually -- but not always -- directly opposite them. Find the high ground. Look for nearby cover. Look for any objects that don't seem to fit -- if it looks remotely high-tech, it's probably spaceship debris. Your goal at this point is to identify a clear direction to move in. If you can't decide on a direct route to the ship, but have it narrowed down to two separate directions, move in a diagonal direction between the two and move toward any alien spawn points you find on the subsequent turn. I refer to this as the kill zone.
Your second task is identifying nearby solid cover. I'm not talking about half-cover tree stumps that will catch fire, or half-cover cars that might explode if you get shot at. I prefer rocks or Jersey barriers (small concrete walls) for their lack of vulnerability. While this doesn't stop Muton plasma grenades, it does stop direct fire -- or at least keeps your men protected. You still aren't moving yet -- you don't know if there's an alien assault coming yet.
Note that each soldier's turn is broken into four phases (or five, with the Run and Gun feat) -- Skill 1, Action 1, Skill 2, Action 2, and then Skill 3 (with Run and Gun). The moment you attack, your turn is over (without the Bullet Storm skill used in the Skill 1 slot). Don't blow a skill on the Skill 1 Phase unless you're certain you will be attacking in Action 1, and you won't have that unit in a position to do more damage on your next turn. Survey your skills, if you haven't, and identify which cover would be best suited to each trooper.
Fourthly, single-move each of your men toward the identified kill zone, utilizing the best cover identified in Step 3. Resist the urge to double-move immediately, unless you decided to burn a run and gun in the Skill 1 slot (which I recommend against). This guide assumes you did not reveal anything in this step. Spread them out so that a grenade or rocket can't drop more than one at a time, and so that you will have guns on anything you reveal.
If you have a rifle-equipped Assault trooper, preferably equipped with the reactionary fire feat down their chain, use Run and Gun and move him into a position with the strongest cover you can muster, and set him to Overwatch if you don't see anything. Additionally, any snipers in the unit that you didn't give the ability to move and fire should move up as far as they can in order to set up for turns 2 and 3, where you will likely encounter the first (and possibly second, and third) wave of aliens.
If neither locate aliens, finish by moving your remaining Assault troopers up on Run and Gun, bring Heavies to the front, and set any Support troopers to Overwatch. My usual composition is 2 Assault, 2 Heavy, 2 Sniper, with a swap to 3 Assault 2 Heavy 1 Support on crashed UFOs. As such, I use an aggressive opening move to move Snipers and Heavies into position, expecting to have to drop or neutralize 3 waves of aliens in 2 turns. If I don't encounter anything as I move up, I set a perimeter around the area I expect to have to assault with overwatching heavies/snipers at appropriate vantage points in order to deny the X-rays movement. The goal is to move into a deployment formation resembling the below:

U.S. Army Ambush Diagram

In this formation, you want a sniper (or heavy, if you're not a fan of snipers) positioned where the flanking security teams are positioned slightly further forward, and you want the rest, your assault element, in the center. From there, Support troopers hold the line, while assault troopers focus on intercepting enemies (particularly chrysalids/muton berserkers) before they reach your flankers.