Technique
There are two styles of skiing - classic and skating.
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 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.
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.
Herringbone - used to go up steep hills.