How does one go about purchasing a new home when they already own one with a mortgage on it?

Gather up all your pennies and come up with 10% down for a new home.

And keep your loans and credit cards paid down as much as possible so you can have little debt...

Sell the old house or rent it out.

If you rent it out, you will need 25-30% equity in the old house in order to have the rental income be used to off set your debt. Otherwise, your income will need to be enough to carry BOTH mortgages.

Since you have refinanced, you can't just walk away. You have a full recourse mortgage and the lender can come after you.

First step is to head to the bank. They can look over everything, and get you pre-aproved for a loan for the new house, and they will set it in lue of the sale of the old house. Since you owe more then its worth, you will have to bring the difference to the closing, however a bank can roll that difference into the new mortgage.

Then, you can focus on selling your houses, and buying your new one, once you sign the sold papers for the old house, you can freely purchase the new home, and hopefully be ready to relocate before the closing happens (Generally 30days from sale).

If you can't sell your current home, you will have to stay there. Some people who are upside down on their mortgages just walk away from them and go into foreclosure but it always catches up with them either by the IRS for taxes, poor credit scores or the lenders.