Dental treatment really requires specialist knowledge, training and expertise. It is relatively cheap & easy to purchase the tools required but I'd say it's definitely not the kind of thing anyone should attempt unless adequately trained, skilled and confident. It might sound very simple and straightforward but it takes a great deal of practise and experience to understand exactly where and how to file for the correct/best results and to also spot any other issues or complications.
When it comes to guinea pig teeth it's also worth remembering that, although the front incisors are relatively easy to access, it's not always a good idea to "adjust" them without also checking/seeing to the back teeth (which are not so easy to get to and work on!)
The CCT runs guinea pig dental courses so some people do choose to undertake some aspects of this work themselves, once they have completed the course.
When guinea pigs require regular ongoing dental treatment it can be very costly to keep visiting the Vet but I think the CCT offers its members free dental treatment, which sounds like a brilliant service for anyone who can get to them.
So in theory it is possible to do it yourself but personally I'd much prefer to leave it to the 'professionals' (i.e. cavy savvy Vet, CCT or experienced Rodentologist) as potential mistakes could seriously affect a pig's health and do more harm than good.