Workbench
You can’t do much without a workbench. You’ll always need a stable, flat, rigid surface to work on and a means of clamping your workpiece to it. You could start with an old table and a vice, or a “workmate”-type small folding bench. Sooner or later, though, you’re going to need a genuine carpenter’s, joiner’s or cabinetmaker’s bench, preferably made of solid beech or some other appropriate hardwood. They can be expensive: upwards of around £400 for a basic bench. But of course you could make your own once you have some basic skills. There are books and plans available to help you.
Clamping tools
You’ll also need some clamping tools. Never try to hold your work down with one hand while you chisel or saw with the other. It’s dangerous.
G-clamps are essential: shaped like the letter G, you turn a threaded handle to apply pressure. Get as many as you can afford, since you’ll never have enough.
Beyond that sash cramps, or a range of modern equivalents, are vital: they’re made up from a long metal beam with sliding stops that you can tighten. Sash cramps are used for holding completed furniture in shape and applying pressure when you’re gluing up.
“Quick grips” are a versatile, in-between solution: bar clamps that you squeeze tight with a trigger.
And holdfasts in various designs are available for holding pieces down on the bench as you work on them.