Its easier if you have a landline.
Otherwise you could get the mobile Broadband connection from Qtel which has data sim and a USB modem. It is only available as a postpaid connection with a monthly charge of 200QR for 3 GB of data. Excess usage is charged in the monthly bill.
There are prepaid internet cards also available..but u need a landline for that..
The El cheapo way is to take a wiFi enabled laptop and go to one of the free wireless hotspots and surf..!!!!
-:)