Making good furniture is mostly a matter of making good parts. Would-be furnituremakers get into trouble when they let little things go when fabricating parts. If a piece isn’t quite straight, a little out of square, or just a bit too big or small, these discrepancies affect far more than that individual piece. Every part of the whole will be thrown off.
These little errors that don’t seem to matter (after all, we’re working with wood, so we don’t need to be that accurate) accumulate. The hope is that they will cancel each other out, but the reality is that they grow together and multiply. If your projects aren’t coming together nicely when assembly time comes around, it is likely that you’re not making good parts from the beginning.
To distinguish good enough from better do it over, you need tools to measure accurately and you need to practice using them. You want sizes to be as close as you can make them, edges to be straight, faces to be flat and corners to be square. You may be completely dedicated to using power tools but you still need to master measuring, checking your parts to make certain the corners are square, and laying out and marking your work.
This isn’t the place to scrimp and try to get by with the cheapest tool you can find. Everything else you do depends directly on your ability to measure and check for square. Buy the best you can afford, and in your shop don’t tolerate the presence of rules or squares that are just a little off.
The first few tools you need are actually machinist’s tools, not cabinetmaker’s tools. A 6” precision ruler and a good combination square moved to the woodshop with the advent of machine woodworking. Absolutely necessary for setting up machines, they also are essential for laying out joinery, and checking your work as a project progresses. The combination square is also one of the best ways to avoid measuring by gauging. In gauging, you transfer distances by direct reference, not by measuring.