Headstock designs are usually trademarked, and it's the most popular place to put the brand and sometimes the model. Checking the headstock shape and doing web searches for anything written on the headstock is a good place to start.
Some places to look for more information, on electric guitars (particularly with bolt-on necks):
- The back of the headstock
- The plate for the neck bolts
- On the body inside the neck pocket (you have to remove the neck)
- On the end of the neck where it would be hidden in the neck pocket (you have to remove the neck)
- On the body inside the pickup cavity (you have to remove the pickguard and/or pickups and/or other electronics
- On a sticker placed in one of those locations (usually only the cheapest guitars use stickers)
The hardest guitars to track down are those that have no model name on them (which is actually fairly common) and that had their serial number on a sticker which has since been damaged or fallen off. At that point, you just have to try to web search the brand name (if available) and try to find it out.
At the end of the day, if you can't find any useful information about a guitar after doing some concerted web searches for the brand name, then the guitar is probably not valuable, the company is probably out of business or was an obscure sub-brand of some other manufacturer, and anything you found out probably would not help much anyway. E.g., there would probably be no OEM replacement parts available for such an obscure guitar.