The first thing you would need to do is to talk with a Mortgage Company/Lender to see if you would qualify to purchase a home while owning a home. The only thing is, you would not qualify for a FHA or a USDA loan because these type loans are for people currently not owning a home. When talking to a lender, they would be able to guide you in the direction they felt would best suit your needs. If you're not sure which lender to use, give me a call and I would be more than happy to give you some names which have been very helpful to my past clients.
I would suggest selling your home first or putting it on the market and in the meantime, looking at homes which may interest you. Once you receive an offer on your home, you will be ahead of the game by knowing which home you're interested in.