I was in the exact same shoes as you about 8 months ago. I'm 24 and bought my duplex in December and am getting married in 5 days! So far it's been an awesome experience getting a duplex, living in one half, and renting out the other. As others have said, getting pre-approved is the first step. Then find a realtor.
The realtor I used for my purchase basically just linked me in on his MLS. I gave him parameters of what areas, budget, and type of home (duplexes). Every day I got emails from him with a couple new houses (or newly priced houses) to browse online. I would suggest doing this so you can get familiar looking at lots of houses and prices online and get a feel for your area. I would also suggest getting a book on landlording to get you ready for that next step.
The house I got was a foreclosure about 8 years old and pretty under market value. The bank had owned it for a while and they'd just dropped the price by $60,000 so it popped up on my radar. The house really only needed cosmetic things: carpet, paint, caulk.. ect. It also needed appliances and a few minor fixes, like broken toilet lids and leaky P traps. I'd never done any kind of handy housework before so it worked out perfectly that this place just needed minor stuff that I could easily learn to do to get a knack for that stuff.
If you can find something like this I would highly recommend it. My two cents are: look at as many properties as you can so you will recognize what is undervalued and overvalued and choose something that needs minor or moderate work (unless of course you're really handy already).
When I was looking people told me that 'you can't go wrong starting out with a duplex'. Well I wouldn't go that far. If you can shoot for getting something that you can pay the mortgage (principle and interest, not including tax/insurance) using the rental income, I think that's a really great benchmark. I am able to pay the mortgage with the rent and it's a wonderful blessing to be effectively mortgage free at 24 :)