What's this antique camera worth?

I'm not sure if it's an antique. It's a Nikkormat FT3.It was only produced for a few months in 1977 (according to Wikipedia… Which I realize is not the most accurate source). My grandpa gave it to me today so I can sell it and get myself new lenses for my Nikon D3100.

How do I know what it's worth?

Check on ebay and see what they are selling for.

Depends on condition, lens and accessories. Check with KEH, they will shoot you a trade in value for the lenses you are looking for. Note you can pretty much double that price for a private sale but you'll need to find the right buyer. The FT3 is a pretty desirable Nikkormat, it is the only one to use AI lenses with wide open metering. But it was quickly replaced by the FM, a much less clunky and more modern design. Note also black paint models sell for more than chrome plated even though paint was a much less robust finish.

My guess is it won't sell enough to buy you even a secondhand digital lens.