Tires look OK from the photo.
Serial number will tell you the year. It might be on the dashboard. My 1964 MF135 diesel had the serial number on a tag attached to the right side of the battery tray. You had to remove the air filter housing to read the number.
Check the bottom of the clutch housing. There's a small weep hole that generally has a loose fitting cotter pin. Check for fluid leakage. A few drops is normal. More leakage might mean a leaking rear main engine seal or a leaking transmission seal.
Check to see if your tractor has Multipower. If it does you'll find a lever on the lower right hand part of the dashboard. Lever down is MP Low range, lever up is MP High range. MP changes the 135 tranny from 6F/2R to 12F/4R via a hydraulic clutch. The MP lever control a hydraulic valve that changes the MP range. The MP on my 135 was stuck in Low range. Didn't stop the tractor from operating. I sold the tractor before I got around to fixing that problem.
With the engine cold, start it and watch the exhaust smoke. Diesels will smoke a few seconds on startup and then the smoke stops. However, if the exhaust smoke continues, check the color. Blue--engine is burning oil (rings, block crack). White--coolant in the cylinders (head gasket, block crack, warped head). Black--fuel system problem.
Carefully check the two stage clutch. You'll find that the clutch pedal is somewhat awkward and takes a lot of leg effort to depress until you get used to it. Check that the pto shift works (three positions--normal, off, ground speed). In pto normal, pto shaft speed is tied to engine rpm. In pto "ground speed" position, pto shaft speed is tied to tire rotation (useful for jobs like seeding).
Check the instrument panel. The Deluxe model has 5 gauges. The Standard model has two gauges. Make sure the gauges are working, especially engine temperature and oil pressure.
Drive the tractor. Run the tranny in all gears. Check the pto and the three point hitch. Get the seller to show you how the draft control works.
Good luck