I'd like to shoot a raspberry pi into orbit. How difficult is this and is this something that could be achieved by hobby rocket scientists?
It is very difficult, and way beyond the ability of hobby rocket science.
To achieve orbit, besides large government agencies, there are very few commercial organisations able to put a payload into orbit.
For amateurs, they do not get anywhere as close. For example, the European record for a student group is getting a rocket to 30km high. Although this is a third of the way to space, it's still nowhere near the speed required to get into an actual orbit.
You can probably achieve 30km with a high-altitude balloon on a hobby budget, but sadly this is nothing like an actual orbit (which is extremely high speed in the horizontal direction).
If you did manage to get a raspberry pi into orbit, it'd likely stop working almost immediately due to temperature extremes. You will also need to include some heating and cooling elements, and either battery or solar panels, etc. The weight of the pi will be a small portion of your total payload weight.
It is possible to put Pi type satellites in orbit, but not by flying your own rocket. Cubesats are a class of satellite specifically designed for this sort of thing, where larger payload owners sublet spare capacity on their launchers to smaller organizations, and get placed in orbit before or after the primary payload is delivered.
Actually building the satellites is not particularly cheap due the the operating environment, and the launch cost varies but is between new car and new sports car sort of money. If you want to go down this path the best method is to look for local education institutions with an active cubsat program.