One of my favorite Youtube channels, 8541 Tactical has started a series of videos that is showing the process of building a 10/22 as a precision rifle trainer. John McQuay is someone that I have always followed and respected as a precision shooter. I have followed his channel since its inception and have learned a great deal.
While I understand that there are many out there that still cannot get .22LR in their area, a .22LR trainer can be an excellent way to train inexpensively, or at the very least, less expensively than shooting 200rds of .308. I have trained with a .22LR for a long time,shooting at 100yds to get an idea of where I can improve my shooting. At 100yds any mistakes become magnified and much easier to see, also being a very light round it is excellent for practicing wind calls.
Check out the first two videos in the series below. If you are just getting into precision rifle shooting, or want to more about precision rifle competitions check out the Youtube channel here: http://www.youtube.com/user/LoneWolfUSMC