There are grooming books you can buy. You can also buy a video. However, the best teacher is experience. They are your dogs, so if you screw up you are the only one who has to look at it, and you can learn more next time. I never went to grooming school, but I groom pets and show dogs professionally. It's something you just "get" after a while. I started when I was a child.
But I think in your case if you go and buy a decent set of clippers, some shears, some GOOD shampoo and cream rinse, and nail clippers, good picn and slicker brushes, and a good comb, you should be all set. You can dry them with your own hair dryer, we use those on show dogs all the time. Just make sure the setting is cool enough. I use "warm" on mine and check the temp all the time.
Any good Lhasa breed book will show you puppy cut patterns. You will also have to get used to holding the clipper (like a pencil) and the shears (only move your thumb, not the whole hand).
The cost of buying all of this will be a lot in the beginning, like maybe two visits to the groomer. But then you will be all set and eventually the equipment will pay for itself. You might want to invest in a grooming table, because they have a non slip surface and a noose and it's much easier to see what you are doing and to have the dog at your level.
You can find what you need at PetEdge, they are probably the cheapest.
Have fun!
Oh, and clipper burn is just what it sounds like. Clippers get HOT and you need to make sure you are not holding it AT the dog's skin and you also need to keep spraying them with Kool Lube or something similar. There is also a TON of maintenence with clippers, getting them sharpened, etc. and you have to make SURE nobody drops your clippers or shears or they are ruined and need to be recalibrated by a professional or replaced.
Adding that IF you just bought a good brush and comb, you could save a ton at the groomer! Just demat them all the time (twice a week) and you can probably get her to reduce the price a LOT. Most of that charge is for dematting and having to deal with a dog that is not kept up. I pro-rate, too, for people who bring their dog in every week or two and I give them a pretty good discount because it's less work for me each time and I would rather bathe and blow out a dog than sit and demat. It's better for EVERYONE. So talk to your current groomer or call around and see if someone will do that for you.