Adding a wireless router to a domain

Adding a wireless router to a domain

We have a domain that every computer connects to (roaming profiles is
enabled as well).
Recently we purchased a wireless router (ASUS RT-N56U), which is connected
directly to the network/domain controller. So far all of our workstations
are connected via ethernet (all get their IPs/DNS/etc. from the DHCP
server automatically), but we'd like to now add workstations wirelessly.
My problem: I'm pretty savvy with computers themselves, but still learning
networking related stuff. How exactly can I get a workstation to connect
to the wireless router, AND have that workstation be able to access files
on the network?
So far I've put the wireless in AP mode, but now duplicates are showing up
in the client status page on the wireless router (for example, two
workstations of the same name - both of which have the exact same MAC
address).
Thank you in advance for your help! Like I said, I'm kind of learning this
stuff, so forgive my ignorance.