Finding a job in a new city is very similar to finding a job in your current city, it just has some extra logistics to it.
You can find job postings in various places; Craigslist, Monster, even check your school and see if any companies are still looking for people. See if there is a job board for your target city. Look up companies in the city and check out their site for job postings. Google the target city name + your job title and see what comes up.
I would suggest that you only apply to a handful of jobs at a time. Choose the companies you want to apply for, research them and think of why you want the job. Write your cover letter letting the employer know that you are looking to move to the city and are looking for the right job and why you think their company/position is a good match.
Once you start getting replies about your applications, see how willing the companies would be to do phone interviews. If the company has a multiple interview process, see if they would be willing to do it all on one day to help with your travel expenses. You'd be surprised how prospective employers are willing to go to help you out if you just ask.
If you get more than one interview and you have to travel, try and make them all on the same day. Again to lower your travel expenses.
In the end, market yourself well, and show that you want to work, and you are willing to move to work for a company. And while you're job hunting, if you have a specific location in mind, start planning your move. You could even look at apartments on the same day you go for interviews.
Good luck!