Hi,
Firstly, if I were you I would consider very carefully in which area you want to work. When you start your first job, you are going to be stuck with it for at least a year - if you leave after a few months, it creates a very negative impact for prospective employers.
There are many ways to start your career as a software engineer - certainly your University has a careers centre that can advise you. They could probably help you with writing your C.V. - having a good one is critical.
However, eventually it is going to come down to getting yourself out there - send your C.V., contact employment agencies, visit websites (as mentioned before, monster is an excellent resource), etc..
Finally, make sure you prepare yourself well for any interviews that you get offered. It really is first impressions that count.
Good luck...