Hi Mlana,
Welcome to Flyertalk.
You have a few options, depending on exactly where you're going (Edinburgh university has a number of locations).
The train is fastest, taking 50 minutes from Edinburgh (Waverley or Haymarket) to Stirling. You'd need to take a bus or taxi either end. It runs every half hour and costs up to £8.30.
There is also the Citylink bus service (timetable
here) which takes 1h10, but has the advantage of some services going directly to Stirling University. It runs every hour (with 3 per day going to the university) and costs up to £8.
The final option is the Megabus, which is actually the Citylink bus, but they resell cheap seats on
http://megabus.co.uk/ You could only get it to Stirling city centre, however, but £2 fares are easy to come by.
For blow-by-blow directions,
http://www.travelinescotland.com/ is very useful.