Sweeping the Battlescape
After deploying from the assault craft, the next stage of combat is to Sweep the Battlescape and clear the area of remaining aliens, as well as find the UFO they landed in. Both UFO Crash Recovery and UFO Ground Assault missions usually follow the same profile.
Sweep And Clear
At the start of the battle, one of your advantages is that the black "fog of war" accurately marks everywhere you haven't checked for alien presence. Don't lose that advantage. If you sweep and clear the battlefield properly, every square that becomes and stays lit will be a square you don't have to check for aliens again. If you have holes in your sweep or perimeter, it's much more of a nightmare to catch that last alien -- not only do you have to check the black areas but also areas you've checked before.
Any battlefield structure which obstructs your view (buildings, orchards, UFOs, etc.) can conceal aliens and must be cleared out carefully. It is best to destroy these structures (using Rocket Launchers, Alien Grenades, or Laser Rifles -- see Destroying Terrain for more details) instead of checking them room-by-room. If you can spare the ammunition, Heavy Plasmas, Blaster Bombs, or Heavy Weapons Platforms can also be used; several of these can also be used to breach inner or outer UFO walls in the final stage of the mission.
Flying aliens can also sometimes pass over the top of a building unobserved, and ground-based units often snipe from rooftops that can be reached by stairs. If a building has multiple floors, you should destroy each of them; aliens can be on any floor, and units on the roof can be more readily spotted once the lower floors are destroyed.
In daytime, your soldiers' visual range is 20 squares. Night Missions are very tricky: your visual range is only 9 squares -- but aliens can still see the full 20 squares away. Use lots of electro-flares or incendiary ammo to illuminate your surroundings, and surround yourself with smoke to eliminate the aliens' advantage.
Move In Sequence
1) Reactions to any enemy action of previous turn (shooting at exposed enemy until dead, grenading concealed enemy and avoiding area, plan medikit use on fatal wounds)
2) HWP scouting run. Exposed enemy engaged by support snipers & heavy weapons.
3) Scouts proceed cautiously. Scanners may be of use outdoors as well as indoors. Exposed enemy engaged by support.
4) HWP and scouts retreat and fire at remaining exposed enemy if necessary, otherwise take cover and save time for reaction fire.
5) Support moves to cover scouts for next movement. Note support often does NOT need to keep time for reaction fire, which helps when trying to get that heavy Rocket Launcher into position.
6) Kneel if possible. End turn. Observe enemy activity and evaluate.
Evaluation should give probable numbers and locations of enemy for next set of orders.
 following the rule of "Never give a discovered alien another turn to shoot at you". I would happily trade my chance at reaction fire to take one more alien out of the equation before the alien turn starts.
Check Those Corners
Keep a tight perimeter, which means everyone is at most about 10-15 squares from their nearest buddy, or any alien hiding between them. If there's a dense thicket or wheatfield to wade through, get closer or burn it down. If there's a barn or other structure between two of your perimeter squad, send in a fireteam and/or explosives to clear it before pushing the perimeter further along.
Cover Your Back
Keep at least two soldiers in the rear both for support fire and to keep a lookout for any aliens trying to sneak through the lines. It is often easy to forget aliens which have been knocked unconscious during your sweep; if they recover before the end of combat, they will wander around behind your perimeter, disarmed, but completely unseen. This is possibly a good task for the Rear Commander.
Snipers at distance are good at countersniping aliens atop lone buildings. Rockets into the building also work. Upper stories are often weaker or more flammable than the ground floor, thus more vulnerable to cannon rounds. Remember fire will take a while to burn anything.
If you can work it into your style of play, bring lots of explosives and chuck them at doors, windows, and rocket-created holes. With enough walls missing, it's a lot easier to check for aliens. Since this isn't a terror mission there's no risk of civilian casualties. (but civilian lives are not a big enough reason to avoid using this tactic during terror missions... a skilled soldier is worth many many civilian lives) And explosives are cheaper than soldiers - even Alien Grenades - just remember to use them.
Flatten those hedges and orchards too. Preferably by grenading the far side.
Never Give Them A Second Shot
You'll occasionally lose soldiers to lucky alien snipers with this doctrine. But it's still good doctrine. By moving only a small bit each turn, with your high-reaction scouts, you've minimized the chance of reaction fire, and by keeping a wide perimeter you've maximized the chances of getting a view of their flanks. Which means you'll be ready with the support fire. Sometimes the aliens hit. Sometimes they miss. Never give them a second shot.
The Beginning of the End
The usual three stages of a ground assault are: Deployment, Sweep, and UFO Breach. Eventually one of your soldiers will spot part of the UFO, which means that you can start planning the final stage - but first you have to finish the sweep properly. Your perimeter should change through the sweep, from a circle expanding away from the Skyranger, to a line touching the map edges, with cleared area behind and uncleared in front, to a circle surrounding the UFO. Proceed at a steady pace and don't rush soldiers into uncleared area. The first soldiers to come within range of the UFO should take up guard positions, behind cover, at a safe distance, preferably where they can set up a UFO exit ambush. If you did your sweep properly they can do this without fear of being shot in the back. The soldiers on the ends of the sweep line now have to hurry up and clear the rest of the map - it may be worth swapping positions so that a faster soldier or HWP can finish the sweep while a marksman with high reactions covers the UFO.
Once the battlefield is secured, several aliens may remain in the UFO. Storming a UFO is often more dangerous than the initial battlefield sweep, and requires its own set own set of tactics. See UFO Ground Assault for more details.
For anything larger than a Medium Scout, it is possible to set up your ambush INSIDE the UFO. Especially during Jungle Missions, (or night missions, or Jungle Missions at night... against ethereals!) it is sometimes safer and easier to just pile a bunch of soldiers into the chokepoint of a UFO and have them guard both the outer and inner doors. Then set the jungle on fire.
Against Battleships, it is advised not to delay breaching the UFO too long, since the aliens have Blaster Launchers, and will gladly spam them to turn your troops into confetti. Sectoids and Ethereals will frequently mind control your weakest Psi soldier, through their abusive "spotting one of your troops lets us mind control ANY soldier" rule. This soldier will then spin around, giving away 80% of your troop deployment, enabling blaster bombs to appear out of nowhere and kill everyone. Against Snakemen, expect a Chryssalid scout to easily spot your troop locations with their 120 TUs, and have a rain of Blaster Bombs shower upon you.