I have a full copy sandbox. I now have a user that wants to explore the org and try some things out however, I don't want them to do this is the production org. Therefore I need to set them up in the sandbox. If I set them up in the Sandbox, will the license allocated to them be taken from my production org licenses?
No, sandboxes do not count against your production license limit. However, within the sandbox you'll still need to stay within your overall limit. Since it's a sandbox, if you run low just deactivate some users who don't need access to the sandbox.
For example, if you have 2 free licenses in production and create a sandbox, you'll start with 2 free licenses in the sandbox. After creating a user in the sandbox you'll have 2 free licenses in production and 1 free in the sandbox. Once you hit the limit in the sandbox you'll need to deactivate users.