For the most part, in my experience, precautions are all fairly common sense.
- Make sure you're in a dry, dust-free and clean environment. Ensuring that you have good access to everything you'll be playing with, and making sure that you're in a well-lit area also helps.
- Depending on exactly what you're doing inside, it might be an idea to ensure that power is off.
- If you remove anything, make sure you know exactly where to put it back, this will avoid the potential problem where you end up with a stack of pieces and no clue what to do with them
- If applying moderate force to a component doesn't work, the solution isn't always the application of more force
If something feels like it's going to snap, there's always the chance that it will. You might need to reconsider your approach and try a different angle, etc.
- Make sure that when you're done, your activities inside the tower haven't dislodged anything important. Check that cables are clear of fans, etc.
Apart from those I can't really think of much, I find that most computers are a bit more resilient than people would have you believe. I can't think of anything apart from what I've mentioned, and so far I'm still alive, and haven't broken anything, so I guess that just about covers it.