If it's a brand name; e.g. Dell, HP, Acer, Gateway; you'd look on the back of the computer case for a "plate" containing things like: model number, product number, serial number.
If it's a custom built computer, you'd get the make and model number of the motherboard; which I think we should skip for now. You'd have to open up the case and start removing components. Even then, it's hard to get a match.