most things are the same when you check any used car but here is some things more applicable to the land cruiser, check the MOT history online\ or the previous mot sheets if present. Check the service history and its not a problem if its been serviced by the owner as longs as his claims are backed by paperwork.
When you look under the car check;
Chassis will have some surface rust here and there which is ok, but it should be solid and generally rust free, the engine bash plate and fuel tank guard generally suffer alot of surface rust. Have a good poke around and check the frame is solid. The rear axles are prone to rusting and when they get really rusted they can become porous so check the axle thoroughly, if its bad, you will need a new rear axle casing. Also check the rear suspension mounts and bump stops as they can rust though...the drain the hole becomes blocked and they fill with water which then rusts away from the inside.
The transfer case, engine, gearbox, front and rear diff should be dry with no leaks..check that you actually have a front and rear prop shaft and just have a look if the grease nipples look like they have seen a grease gun. Grab the prop shafts and try to push them up and down and side to side, you should have no play then grab the shaft and try to rotate it, you should only feel the play through the drive line not in the prop itself...if there is any play you will need to replace the universal joints..Some people also use a screwdriver to check them. Have a look at the steering rack and that its not leaking and the gators are in good condition, Give the steering rack a good shake to check its secure and the bushes are not worn, then check the all the suspension components are in good condition. The rear door hinges brackets can become loose which results in the back door banging...it should just tighten up to cure it. Check the brake pipes and also check the two coolant pipes which lead to the rear heater as these pipes are prone to leaking. Some people replace the pipes with black hose or they might just bypass the rear heater by joining the pipes in the engine bay together.
put the car in HL check the CDL lights up you may need to drive forward a few feet, then put the car in low ratio and engage the difflock, when it engages the red light should change from flashing to a solid light...if it does not change to a solid light either the switch is U/S or most likely the rear diff lock needs replacing...when its engaged the ABS light will also come on which is normal, turn in a tight circle...you should hear some scrubbing...but no knocks or bangs in the driveline ( only drive very short on tarmac or you can suffer transmission windup and make something go pop! ) do the same in HL.. then test drive the car as you normally would. check the parking brake as they are prone to seizing up through poor design and though not much use on automatics...on the test drive you should not hear any transmission whine or knocks...The 4 speed auto should change gear smoothly and the torque converter locks up above 54mph...but the revs will drop off if you take your foot of the gas.
Under the bonnet, check the gearbox oil is nice and red...and that the oil does not smell burnt or is black/dark in colour...or is pinky, check the condition of the front radiator and the colour of the coolant is also nice and red...any pinkness could be a failure of the radiator/oil cooler. Toyota designed the oil cooler for the auto box to be built into the radiator and they are prone to leaking which causes fluids mixing resulting in either your autobox overheating or the engine...either way, if it does not cook the clutch packs in the autobox it will take many flushes to get the box free from contamination. Before you start the car up... give the fuel primer a few pumps which should be firm to press, if its loose and you have to pump it a few times, it could mean there is a leak in the fuel line somewhere. Check the power steering fluid level...the fluid in the power steering is ATF dexron 3 so it should be red or mo
What I wanted to ask was, what should I be looking out for when I come to buy one? Are there any common faults that I should be checking?
just what came into my head so it could have been worded better 
but I do struggle explaining whats on my mind to words from my mouth 
Thanks again!
