* big caps that can contain high voltages even when a device is powered off, in TVs or microwaves.
* Know where a fire extinguisher etc is, keep them near the workbench.
* Keep the workbench clean, tidy and well-vented.
* Don't panic when mistakes are made. Slow down instead of doing a quick-fix.
* I like a big red button to power down everything instantly. Can be just a switch on a plug box.
Risks to consider in general are (also of the top of my head don't take as exhaustive):
* Electrocution
* Burning yourself
* Setting stuff on fire
* Fumes, both from soldering and overheating/burning plastic
There's a kind of balance between habits and awareness. Rely too much on awareness and you will miss some safety issue during a complicated repair. You need good habits, but rely too much on them and you won't notice when you finally make a mistake.
Those apply during repair processes. It's also possible to render a device unsafe to use, for example by damaging a li-ion battery or by a 'bodge' repair that circumvents a safety feature.
Reminds me of the comments I read on a video of somebody doing something unsafe - "safety squint".
* an isolation transformer - meaning you must now touch both conductors to get shocked instead of just the live one
* a foot switch to control the power supply - serves as a "dead man's switch" to cut power in case of an accident
(these are not mutually-exclusive, you can combine them)
Apart from that, just fix broken stuff. Practice like any other skill, like others have said.
Like decide what skills to learn based on what’s broken.
Need to solder something together? Buy the soldering iron. Need to figure out which capacitor you need to replace with? Learn how to identify capacitors and navigate digikey.com