Your best bet would be to take a denter and mechanic with you when you check, because their experience is beaten by none. There's no one set of rules because each car is different, but you can check the following things.
Documents
Check for original file and registration. Check if the car has indeed been transferred to the person you're purchasing the car from (open letter cars are more difficult to transfer in your name since recently). Check if all tokens have been paid.
Body
Determine the level of body work done (denting + paint). You may be ok with a paint shower or a some scratches and small dents. Check pillars for any major accident history. Also, check windshield rubber and other windows for any anomaly. Check for cracks in the windshield. Check for permanent body joints, especially the ones with machine welding (e.g. two points a.k.a. cups under the hood where the hub for front wheel shocks is attached). Check for any rust on the floors, under the hood and in the diggy.
Engine:
Most ppl rev the engine to higher rpm and see if gray smoke comes out of the exhaust. I'm not sure how effective this procedure is. Another way is to drive the car and check if it has a good pick on gas and petrol. Also check the gauges for any heat up etc. (usually not possible due to short time available for checking).
Suspension:
Check if tires are in proper/ acceptable condition and same size/ brand. Drive the car, get to a clean and preferably long stretch of road. Get the car to the speed of around 60-70 kmph, release the steering wheel and see if the car stays on the same line or takes a particular direction. Might indicate an issue with suspension/ alignment (camber) or tires. It's not a big issue and usually plays a less important part in car purchase decisions.
AC/ CNG:
Obvious checks are convert from petrol to CNG and back again to see if it starts and runs properly on both. Also check if AC is running properly, cooling the car, not putting too much load on engine and the rpms stay stable, no heat ups. Again, it's a minor issue. Not a deal breaker.
This is the basic stuff. I'm sure experts will come to your rescue in a while. But do keep in mind to give them a little time and never create a new thread if no body is paying attention to the old one. Bump the old one after waiting for at least around 24 hours.