There are two styles of skiing - classic and skating. A great overview of all of the techniques that includes very detailed information can be found on the Team Aker Daehlie website.
Skate Skiing
Skate skiing uses several techniques, depending on whether skiers are going up hill, down hill, or skiing on flat or gently sloping terrain.
V1 - used to go up hill. See examples here (6:21), here, and here.
V2 - used for power on flat terrain and gentle uphills. More advanced skiers will use V2 on steeper uphills. See examples of V2 here, here and here (8:29). See here (9:30) for transition from V2 to V1.
V2 Alternate/Open-Field - used on flat terrain and gentle downhills. This technique is a great way to save strength on longer skis. See examples of V2 Alternate here (3:50), here, and here (8:47).
V0/No-pole skate - used for power on downhills. See examples here (3:22).
Classic Skiing
Classic skiing also uses several techniques, depending on whether skiers are going up hill, down hill, or skiing on flat or gently sloping terrain.
Striding - used to go up hill. See examples here (4:32) and here. See analysis here.
Kick double pole - used on slight uphills or flats. See examples here (5:21) and here.
Double-pole - used on flats. See examples here (1:35) and here. See analysis here.
Herringbone - used to go up steep hills. See analysis here.