Shift the chain to the big chainring and then pluck at it, pulling it forward from the middle of the chainwheel. If it pulls out enough so you can see light between the chainring and the links of the chain, the chain is probably stretched out enough to need replacement.
At any rate, you will need a chain tool to "break" the old chain and remove it from the bike. Then, if you decide to re-use it (if it isn't too stretched out) you can soak it for a few hours in a coffee-can full of orange soda. That works pretty well to dissolve rust; not as well as more expensive stuff, but tolerably. A wire brush may help.
(Oh, and if you have a bit of extra bikechain lying around, practice with the chain tool. )
If you buy a new chain, go for an ordinary chain for a 5-8 speed cassette. You can get this kind of stuff online easily. If you get one with a so-called "powerlink" you'll have an easier time putting it on the bike. But you'll still need your chain tool because they always ship new chains with too many links and you'll have to remove a few.
Others have said you may need to replace the cassette (rear gears) and chainrings (front gears) if the bike has been ridden hard for a long time with a stretched chain. Happened to me once. Pain in the neck. May or may not cost more than the bike is worth.
If you get this chain situation fixed and you decide you like the bike, consider changing the brake pads, brake cables and housings, and shifter cables and housings. In the 21st century you can watch online videos showing how to do all this stuff.
I know all this because I do a bike clinic every year with the kiddos at our local public housing project. We pick through the bikes -- mostly cheap mart bikes -- that the cops picked up, and fix up the best ones.
Have fun! It's really cool to be able to care for bikes.