We will start with the guaranteed uphill techniques that can get anyone over any hill and progress to the speed techniques used by those racers with hollow bones and negative gravity potential.
The basic technique is the herringbone, the no-glide V stroke. When the hill gets steep your skis turn outward and you stop. What you have done is create a stable platform where you are standing straight up and down on your skis. It is very easy on soft snow. On icy snow you will need to stomp down a bit to create that stable platform. Next time you are out skiing and an uphill gets too hard just stop and stand there in your V-zero and think how nice it is to be outside on such a beautiful day.
To move up the hill, stand on one ski and step up the hill to the other ski. Poles are behind you and provide a bit of a push. A coach can maybe help you a bit with exact angle of the knee and ankle, and how to get more push from the poles, but it is really very simple if you just relax and take your time. You will get to the top.
With skate skiing the next variation is the herringbone skate also known as the diagonal skate. Take the skier above and add a bit of glide to each step. That means you go uphill a bit more with each step, so you take fewer steps. It is a very good technique for very steep hills, and for days you just don't have the oomph to keep a V1 going. There are also times on the flats when conditions are very bumpy or there is soft deep snow that the herringbone skate is just easier than anything else.
The following skier shows what is also known as the "flying herringbone"
We will deal with other uphill skate techniques at other times. Those aren't easy.
With classic skiing there are two other techniques.
The basic technique is the diagonal stride. With good technique and good wax you can get up many hills. Conditions are often better for kick out of the track, learn to test that out as you ski along. If the track is glazed or your wax is slipping, try outside the track.
The next transition to learn is the half-herringbone. When you have some kick, but start slipping, angle one ski in a herringbone and keep the other in the track. You will get the stable uphill push from the herringbone, while still getting glide legally on one side. In classic racing you can be disqualified for gliding both sides of the herringbone, but not for gliding one side in the track. It is a very effective and restful technique for getting through hilly trails.
I was unable to find a picture of the half-herringbone, but will watch for them in race picture sets throughout the year. I would encourage you all to start looking at the picture sets on skinnyski.com throughout the race season. We are blessed in Minnesota to have skinnyski.com as a resource. In the old days when I was a young fat slow skier we would drive around looking for random patches of snow, or call the ski shops hoping for some info on a skiable patch. Now, we just go online and find out up to date info.