Xbox live setup help

I know you guys are gonna think i'm a noob and stuff for asking this, but please dont be mean, it will make me cry...anyways i have been trying to set up my xbox live on my 360, and i haven't been able to here's what i have...

An ethernet cable (the one it came with)

A computer with a wireless internet adapter that goes downstairs into my mom's computer, where the wireless router is

So i was wondering how to set it up Can i plug the ethernet cable directly in to my computers Ethernet slot? or do i need a wireless internet adapter for my Xbox?

Thanks in advance:?

Yes you can but you need to set up the computer as a router for your 360.

Much easier just to connect the 360 to your router or get the wireless thingy for the 360.