How can I use my t-mobile broadband stick with linux on my Asus eeepc 701?
It is configured for Windows and Mac OS only.
The stick is a Huawei model E160 HSDPA USB stick.

Have you seen here: http://wiki.eeeuser.com/ ?
Particularly this part: http://wiki.eeeuser.com/howto:use3mobilebroadband
It works out-of-the-box with the E220, and should with the E160, otherwise, check the forums

I'll just add that I've personally had some trouble with getting the IP addresses through DHCP with some of these Huawei modems; I'm not completely sure what caused it, but I had a few cases where the device was recognized, it worked fine as a modem, forming some kind of a connection, but didn't ever get the DNS server addresses for example. From what I could make out of it, it looked like some of the set-up was being done in a bad order (or perhaps with too small timeouts?), but in the end I had to manually specify the DNS addresses to make it work. Even worse, every time it connected it tried to fetch the addresses through DHCP and overwrote the resolv.conf, causing it to look like it didn't work. Back then my quick&dirty solution was to script the connection so that the overwritten file was replaced with a backup copy containing the correct addresses after everything else was fine. And no, for a reason I don't understand, even telling the system that I wanted to set the addresses manually didn't work

I don't mean to scare you off or anything; probably your Huawei works just perfectly with your Eee (and my problems were due to malfunctioning software, drivers or something), but just in case -- if it seems to work but you can't reach external machines, check that it got the address information right.