Hahaha difficult to explain and learn in just using 1 tread reply leh! Basically needs a sharp eye and experience too which I cannot just teach you like that. Anyway in a nutshell:
1. When you see the car for the first time, don't tell them to start it first. This allows you to inspect when the car is still cold so you can check thoroughly.
2. Inspect the exterior if got signs of accidents. This is not easy coz need a keen eye and experience to see the minute details like slightly different paint surface or shade, clear coat borders, alignment between panels. Check also for signs of flooding like dirt & rust, usually underneath the carpets and lower part of the firewall inside the engine bay.
3. inspect beneath the skin like opening the boot and the engine bay and look at the minute irregularities (such as some irregular paint spill over or chipping, or bent beams, broken light mountings, etc2.) to detect further signs of accidents. Open all the doors then also check the beams & pillars if all still aligned nicely and to see if there's any clear coat borders or seperation. If got then that indicates the section around it have been repainted for whatever reason.
4. If all above ok, means you're pretty confident the car is not yet suffering from major accidents or flooding, then check the engine while it's still cold. Open the oil cap, radiator cap, brake fluid cap and see if they're all look nice and clean. Take out the oil dip stick and see the oil condition if still ok. (this is not possible for some BMW cars coz some don't have a dipstick, go figure!) Check for signs of leaking around the engine (this might be almost impossible if you buy from a dealer coz they would have clean it up but still do it anyway, just in case they miss a spot).
5. Inspect brakes if still thick enough (might not be possible to see the brake pads and discs if the rims is pretty closed design though).
6. Check the tires if still in good condition, this can be a bargaining point for later.
7. Now start the car, pay attention to all the instrument cluster if got any abnormal lights showing (like check engine light or VSC light or whatever warning light that is not supposed to be on after the engine is fired up). Then go back to the engine bay and listen for any strange sounds. Then go back into the driver seat and rev the engine gently and listen to it if still sounding smooth. Then turn on the aircon and still listen if still smooth and aircon is cold. Check all the lights, electronics, and buttons if they're all functioning as expected.
8. If all that ok then try get familiar quickly with the controls and time to test drive. When test drive, do not turn on any radio/music and try to go thru a bit rough roads to listen for any rattles and noises. Then try to push the car a bit to see how is the power and response and also test a bit hard braking to see the ABS working (just be careful when doing all this). If possible push/rev the car until redline in some gears to make sure it's still working fine even when at max rev. Feel the steering and how it handles if you like it or not.
9. If all this ok then only nego the price down, use all the flaws that you can find during your inspection to nego down! If the answers to any of the steps above are not ok then you can just stop at that point and leave coz you might have found a bad one.

My suggestion is you need to bring someone who knows all these to help you check out the car properly coz I doubt you can do all these as a first timer already. Or bring your trusted mechanic so he can plug in a diagnose tool to also check the car electronically to see any error codes popping up.