Car was owned by a grandfather and never used very much. Kept in a garage and never used during cold or rain. Now I want to use the car, but hesitate due to concerns about seals and tires, etc. Can you inspect and learn very much about the condition?
Yes, you can do an inspection and learn a lot about it's condition. If you're not familiar with what to check, it may be worth getting an expert to have a look over it (if it's a classic car, your local owner's club will often have plenty of enthusiastic members who would be happy to tell you what it needs)
As a guide:
Tyres - these will probably have perished (cracking in the rubber), so I'd recommend replacing them - certainly do so if they are more than 8 years old or so.
Hoses & Belts - also probably worth replacing - brake lines, coolant hoses, fuel hoses, timing and alternator belts, any other rubber components
Brakes - if it's been standing for a long time, these may well have siezed, and will need rebuilding. I'd also suggest changing the brake fluid, pads/shoes and discs.
Fuel - any fuel in the tank will have 'gone off' if it's been standing, so you may need to drain it and refill with fresh fuel.
Engine - give this a full service, new oil, filters, plugs, leads etc. Turn it over by hand (using a socket on the end of a long bar, or put the car in first or reverse and push it) before trying to start it, in case it's siezed. Change the coolant and flush the radiator.
Battery - again, if it has been standing, this will probably have expired - I'd replace it as a matter of course.
Other than that, it will probably just need a good clean to get rid of all the dust!
Sounds like grandad looked after his stuff. So despite what looks like low mileage, it could have been serviced regularly. Check over any paperwork he may have stored, or if he's still about then ask him about service history.
NickC's answer is a good list of things to look at, but inspect before just replacing. I'd suggest putting a voltmeter on the battery, and get a reading. If its over 10.5 Volts then the battery is probably okay but flat, so connect to a trickle charger for at least a couple days.
Tyres - check for cracks, then inflate to pressure (lower pressure helps show cracks) Since its been garaged its probably much less exposed to direct UV.
Environment - check the floor of the garage for stains and leaks. If there's something leaking it will either puddle on the floor or hang underneath and make a damp area. That will give you a clue to whatever might be leaking.
Fuel - Check the carb or fuel pump and try to get a smell of the petrol/gas. If it smells weird its going to be off, so drain the tank and fill with fresh then expect it to take a while to catch when starting, as the old fuel in the line fails to burn.
Oil - its going to be hard to change cold motor oil. If the dipstick looks black then drain out what you can, fill with cheap oil, and change it again in a couple of days once you get it running. If the oil in there looks okay then its good enough for now.
In short, check everything, then top up fluids. Start it and leave idling for ~5 minutes to settle down, and then try some gentle manoevers in the driveway. Be mindful that there could be poor/no brakes, so keep a hand on the handbrake/emergency brake/parking brake.
If that all feels good, then take it around the block, nice and quietly. ONLY once its fully warmed up and going nicely, then tap the pedal and give it some revs in neutral
Driving an `80s vehicle
This might be a different question, but in brief expect some surprises if you're used to a more modern vehicle.
Cold starts - Its not impossible that this vehicle has a choke, if so it needs some manual assistance to get the mixture right for a cold start. Run it gently for the first few miles to reduce your fuel usage and emissions. Gradually push the choke into the dash as motor warms.
Brakes - will be worse than a modern car. It won't have ABS or any of that flash stuff. At best it may have some rudimentary brake assistance system, a precursor to ABS, and a power servo. Assuming pads or shoes are in good condition you will be able to lock the brakes; and in an emergency you might just do that. Upshot increase your following distances
Fuel - Not sure where you are in the world, but this car may be old enough to require lead-replacement additive if it lacks hardened valve seats in the head. In my country we have cheaper 91, 96, and sometimes 98 octane fuel. If this vehicle is tuned for 96 or 98 then it will pink and knock running on 91. Use the right fuel.
Steering - It might have power steering, or might not. Old power steering should work fine, but it gets real heavy real fast if the motor stops or the system looses pressure.
One other thing bears checking...
While it may not seem like a big deal, if the rust gets serious enough, it can literally eat holes through the floor of the vehicle. I saw one car from the 80's on which you could literally stick your foot through the floor if you weren't careful.
Seriously, since it was kept in a garage, I expect this is not a problem at all, but I would just check out how the basic frame is doing, and make sure you aren't running a risk of losing your exhaust pipe or something along those lines. Check your rust level before it's too late.
*Perhaps a bit of bias here, since we have big time problems with that here...
Im not a mechan a number of long-termn deployments or general trips away from my car which is quite old. Here is what I've learned to be aware of.
Tires - The number of times I've come home and found that there was a slowleak in my tire that didnt deflate until in certain position is well. Other time it was just old tires.
Battery - Generally speaking if it's a domestic car. They have always on cigarette lighters (which I love). I've had my car parked for so long while a charger was sitting in there that this completely killed the battery. You can recharge the battery normally speaking
Fuses - replace any old worn or blown fuses that may control sensors or internal electronics headlights
Also agree with anonymous2 about rust! Sitting in the rain and/or snow it may have developed some corroded metallic parts. Generally around the wheel area. Though on the underside too. I've had a corroded gas line, that was leaking during my drive old vehicle. It was very dangerous.
head and taillights - may not be obvious but generally speaking people may not notice. Especially the CHMSL. Those often go ignored and it can be not legal to drive in some cities with it out.
rubber hoses, rubber gaskets, pans, and other liquid containers and transports - these often fail and get worn out over use and history. Furthermore, you dont want to be driving just to realize there is a leak in it and you've driven 1000 miles with the stuff missing.