A second-hand bike is often real value, but a few checks before buying catch most of the problems that turn a bargain into an expensive repair bill.
Check the frame for cracks or dents, especially around the welds and near the bottom bracket — a cracked frame is not safely repairable on most everyday bikes. Spin each wheel and watch it pass a fixed point; a visible wobble suggests a bent rim or loose spokes. Squeeze both brakes and check they engage firmly, and check the chain and cassette for rust or heavy wear.
Ask how old the bike is and how it was stored — a bike kept indoors ages very differently from one left outside through monsoons. And always test-ride before buying if at all possible; a bike can look fine standing still and still feel wrong to actually ride.