Battery-powered electronics is one of the more forgiving hobbies you can pick up. A 9 volt battery will not hurt you through dry skin. The things that do cause injuries at a beginner's bench are more ordinary, and all of them are avoidable.
What actually goes wrong
- Shorted batteries. A wire straight across a battery gets hot fast. Lithium cells can vent or catch fire, so never short them, never charge them with an improvised charger, and store them so the terminals cannot touch metal.
- Soldering iron burns. The tip runs at over 300 °C. Keep the iron in its stand, never in your lap, and never catch one that falls.
- Flying lead clippings. Trimmed component leads leave the cutters at speed. Wear safety glasses, and hold the lead while you cut.
- Reversed electrolytic capacitors. Connected backwards, or above their rated voltage, they can burst. Check the stripe before you apply power.
- Fumes. Solder flux smoke is an irritant. Work with a window open or a small fan pulling the smoke away from your face, and wash your hands afterwards.
The one firm rule
Stay away from mains voltage until you have proper training. Power your projects from batteries or from a certified, enclosed plug-in adapter, and never open equipment that plugs into the wall. Everything in a beginner's book can be built without touching the mains.
Habits that cost nothing
Disconnect power before you change a circuit. Keep drinks off the bench. If a part gets hot or you smell something, pull the battery first and investigate second.
If you want the fundamentals in one place, with hand-drawn diagrams, start with Getting Started in Electronics, or browse all four books.