Find a good online DIY source that you trust. I recommend This Old House for detailed and easy-to-understand instructions on common plumbing repairs you can do yourself. Make sure you know where to locate the main water supply and the supply to each plumbing application, which is typically located under a sink or behind the toilet. Lastly, familiarize yourself with local codes and regulations. Some municipalities require that you hire a certified plumber for certain plumbing jobs.
The next day, I had an unrelated incident with a sprinkler valve inlet pipe rupturing, due to corrosion (galvanized pipe. Since this situation caused me to lose water service to the house, Charlie sent someone over that day to do an emergency cap off. It was then explained what could be done to provide a permanent fix (basically replacing the old galvanized pipe and creating a new sprinkler valve manifold). A quote was given and the full repair was scheduled for the following day. All is good now, and the job came out $120 below the estimate.
A leaky faucet can be a relatively easy fix depending on the type of faucet, so get to know the basic types of faucets and how to take them apart. You can look for instructions online; YouTube videos are the most useful. A slow drip usually means that all you have to replace is a washer, but make sure you know which size you need before buying a new one.