I have recently inherited a 1962 Buick Skylark. It has not been driven in several years. I know it had a minor radiator leak but otherwise was in very good running condition. What plan should I follow to get it running...what do I do first/
I do not want to put in a battery and turn the key and cause some irrepairable damage.
The gas in the vehicle has long since turned into varnish after several years of sitting idle. So the entire fuel system will have to be rebuilt/cleaned from the gas tank to the carburator.
You need to find a Glenn’s, Motor, or Chilton’s repair manual from the era. I listed them in order of preference. Ebay may be your only bet now to find one. If you visit some vintage car sites, especially one dedicated to your model or manufacturer of the era, they may have a downloadable pdf that someone scanned.
Most GM engines of the era had a gear on the end of the distributor that also turned the oil pump. After changing the oil, you could pull the distributor (make sure you know how to get it back in and time it), insert a long flat bladed screwdriver, sans handle, into the oil pump shaft and chuck it up in a drill and pre oil the engine. Then, with the plugs removed, squirt a little oil in each cylinder.
Then do what Tester suggested.