Plumbing problems at home can be a huge headache. What problems are you able to fix, and what issues will likely require a plumber?
A dripping faucet is something you might be able to YouTube and fix it yourself. However, if it is a newer faucet you may need to call in a professional. Some newer faucets don't have washers, which can make the repair more complicated.
Is the water flow in your shower not enough? It might be an easy fix. It's possible there is mineral scale and other debris built up on the shower head. If that's the case, you can simply remove the shower head and remove the buildup. If that doesn't fix it, then it's time to call the plumber.
If you have a pipe that bursts, the only step you should do on your own is shutting off the water. Burst pipes should be handled by the professionals. In fact, for insurance reasons, you probably shouldn't even try to fix anything on your own.