Welcome to EH-Net. Hopefully coming here at such a young age will lead you down the ethical path in the future. That being said, your teacher has presented what seems like an isolated environment for you guys to have some fun.
A firewall on your system is a great first start. I don't know Comodo well, but there is someting called the Stealth Wizard. There are mixed results reported on their forum. But try to get some stealth, so that the other classmates won't even see you on the network during their scans of the network. Then try Nmap yourself to find your targets and other useful info. I'm not going to tell you how. That is your homework to do.
Next, are these machines configured identically? If so, use that to your advantage. Change your admin password, then use the old admin password on other machines. If your machine is running remote desktop, then so are the others. Deny RDP on your machine and login to theirs.
Without knowing OS version, apps on the machine, etc. I can't give too many specific recommendations. I can guess XP since their is a My Docs folder, but I don't know SP or patch level. Plus, I don't want to do your homework for you.
Try doing a little research on null sessions in Windows XP, fgdump and 0phcrack or Cain.
Kudos to your teacher. I'd like to meet him/her.
Let us know how it goes.
CISSP, MCSE, CSTA, Security+ SME