I have a LinkSys router with one PC connected to it via wireless.  I
want to connect another PC, but it's asking for the network key, which
I don't know.

So I'd like to either find out what the key is, or set a new one.

Can someone tell me how to do that?

thanks!

Network key? Do you mean the 'WEP','WPA' key? 

The 'WEP' or 'WPA' or whichever security key you have is a password that is encryt 
by the router using various technology. So, I assume that you have a
password set and you dont know what it is.

What you need to do is to login to you router's control panel (you can
do so by entering 192.168.1.1 in your browser) You will be prompted
for your user and password. By default linksys has put its username
blank and the password as 'admin'. Then, go under wireless security
and choose the Security mode.

You will be asked to enter a Passphrase and key will be generated. The
key is the 'password' that your computer will ask you if you were to
access the net through your router. If you do not have the key, it
will turn down your request. Thus, making you not able to use the
router.

This feature is used to protect your own wireless network from others
unortherised person from using.

Hope this helps. This is my first comment in Google anwser. =D

If you were to pull the power connection out of the router and then
push in the reset button on the back, plug in the connector and count
to 30 you will have reset the router to its unsecured mode. Now you
can get any number of computers to talk to the router. Of course so
can anyone else. If security is an issue for you (and it probably is)
go to www.linksys.com and follow the very easy instuctions to secure
your network.