This is actually becoming quite common for people to rent their current home and buy a new one. As Christopher says, the first step is to work with your lender and see if you can get qualified for a new loan while renting out your current home. Another early step is to check with the Home Owners Association and confirm that they allow rentals. Many HOA's are putting restrictions in place.
I would recommend that you find a Realtor that has experience with their own rental properties to walk you through the processes involved with being a successful landlord. I have 4 townhouses that I rent out and I know many other Realtors do as well.
Bill Wallace - RE/MAX Results