Does the gear cluster on your rear wheel have a lockring on the outside like this? That's a cassette. Otherwise you may have a freewheel. Give us a closeup shot of this part and we can tell you more.
>>1245637You still have to cut the chain to length, and a chain tool is the easiest way to do that. Alternatively, your LBS might let you borrow their chain tool for free or cut it to length if you mark it off for them.