Lots of great stuff here already.
Safety: NEVER get under a vehicle held up by a jack, especially hydraulic. ALWAYS support properly with correctly sized (or oversized) jack stands. People die every year from having a car land on them when a jack fails.
My Dad (retired machinist and toolmaker) taught me that no job is done until the tools are clean and put away. As I grow older, I have taught myself that the molded toolboxes (one space for each specific tool) is the best way to know if a tool is still AWOL (I used to think open boxes were a better use of space).
On brake jobs on my own vehicles, long, long ago I learned not to put anything replaceable back onto the vehicle. Don't just replace the pads: Do the rotors, calipers, hardware, drums, flex lines, etc. Expect the steel lines to be bad and replace (more recently, I learned to replace with CuNi). Buy all of this before jacking up the vehicle.
Don't replace a serpentine belt without a tensioner at minimum, and possibly an idler pulley ready to install.
Battery cables like to corrode from within, where you might not be able to see the corrosion easily. I once had a shop replace a battery, and got stuck the same week with a dead battery because the cable was bad, and he didn't check/clean/replace it.
Before doing a job for the first time, research, research, research. Before the internet, I would buy both Chilton and Haynes manuals for my vehicles (OEM shop manuals would be even better). I'd always write the tool sizes in the margin as I removed parts, helped with reassembly and in case the job needed to be done again down the road (I tend to keep vehicles longer than most people).
As mentioned above, read forums. Not mentioned, but equally valuable, watch YouTube videos for specific repairs. Be careful with YouTube: Many videos posted by weekend warriors are horrible advice. Read the comments, people are pretty good at policing those things.
Never rule out a root cause just because you already "fixed" that part. New parts out of the box can be bad (especially electrical, thermostats, etc.). I once rebuilt a carb, the engine still didn't run right, and I ignored the carb because I'd already cleaned and rebuilt it. Of course, I missed a jet, which was still blocked...
I'm probably forgetting a bunch.
Mike