I have a Nikon D5100 and a MC-DC2 remote. I'd like to use the remote to hold the shutter open until I release the button, however I don't see an option for this. Is this something that I can do?
This is called "Bulb Mode".
On most DSLRs (including the D5100), you would change to shutter priority or manual mode and slide the shutter speed larger until it reads "Bulb" or something of the sort.