Yes, it's totally possible. That's how I got started. There are all sorts of online references that you can use for the more tricky parts, such as installing pickups and electronics. If you choose to use an active pre-amp, then most pre-amps will include detailed instructions on how to get everything connected. (Audere is a great example.)
A few tips to get started:
- Learn how to drill pilot holes: slowly, safely, carefully and accurately. If you have a drill press it can be easier, but it's not necessary. This comes in handy in various places, such as the holes for the tuner screws, pickup screws and strap nuts (or strap locks).
- Plan out your pickup(s), controls and electronics. Plan on changing pickups once more after you get the first version installed and tested, just in case you don't like the tone or want something different. If swapping frequently is your destiny, consider using screw terminals (instead of solder) to make replacement easier later on.
- Take your time when it comes to shielding the pickup cavity. Measure twice, cut once. Plan on buying extra adhesive-backed copper so you can rip it out and replace it, if the first application doesn't look neat enough. (My first attempt was ugly!) Alternately, consider using the conductive paint that many luthiers use these days.
- Use the Planet Waves gold-plated jacks that Warmoth sells. They are very high quality and will last longer than most other jacks, even after repeated use. These need a 7/8" side jack hole, and a cover plate (either football-shaped or square). Buy a few extra, just in case.
Good luck, and don't hesitate to ask more questions!