Not sure why everybody's being so dismissive of you here, it's a good question you're asking
Ok so first up you want to check around the exterior to see if the car's in good condition -- any scratches / bumps that look more than just the car being thrown in a hedge to let someone by should be inquired about.
Check around for rust.
Check the oil - just use the dipstick for this
Check all fluids if possible, brakes, coolant etc. This isn't possible on all cars (on mine it requires a lot of labour to access the tanks)
Turn on the lights, and check they all work, especially brake and fogs, as you never see those yourself.
Check the tyres, do they have enough tread, and are they inflated?
Moving on to the driveDon't buy unless you can test drive.
You want to have as long of an MOT as possible. I usually go for 10 months minimum, or ask the dealer if they can get it checked and extended.
Make sure you can get a cold start. Otherwise come back later. Lots of issues can be revealed by starting a cold engine.
When you first start the car, does it make any noises? If there is a squeaking / screaming sound, it's likely just the engine's timing belt. Try to inspect this if possible - it could be (and is usually) just loose, so isn't much of an issue, however if it has any damage, try to get a quote from a mechanic as to how much it would cost, and then decide if you still want to buy; it usually doesn't cost much (do this after the drive). This article has more info:
https://www.dumblittleman.com/how-do-i-stop-my-belt-from-squeaking-when-i-start-my-car/Clutch; how high is the bite point? Will it need replacing soon? Does the car slip out of gear?
Check the controls: Windows working? Windscreen wipers, high beams? etc.
Fuel system okay? Check the mpg. Is it lower than it should be? Is anything leaking?
At some point in the test drive you want to hit 70 - this obviously isn't essential but high speeds can expose any problems with the car; try to get on a motorway / dual carriageway if possible. If you hear any unusual sounds try to find their source, and decide whether they need fixing. Here's another article:
https://www.bankrate.com/finance/money-guides/16-costly-car-noises-1.aspxStick around in the gears for a bit while accelerating. This may expose any problems that occur when the vehicle is at higher revs. This could potentially be allowed to let slide if its really not important. I, for example, tend to short shift when driving to college as my commute is 75 miles (round) and fuel economy is everything. However, there's a lot of joy to be had in driving quickly
Suspension - is everything smooth?
This is all I can think of in all honesty, however it definitely isn't a comprehensive list. If you're spending a lot, see about hiring a local mechanic to inspect the car for you; this may cost a few hundred pounds though.
None of the problems on this list should be dealbreakers. See how much the issue would cost to be fixed (if it needs to be) and then weigh that up with the price of the car, and what you could get another for form a competitor.
A lot of it is common sense too.
Good luck!