Mortgage consolidation is generally done through a refinance. Essentially, what this means is that you take out entirely new financing on the home and you then use the money from this new loan to pay off both of your old loans. This can be a good idea if you have a first and second mortgage on your home, since you can then roll all of these into one loan that you will need to pay back instead of having multiple loans.
The process will require you to qualify for a refinance loan. This means that you'll need to find a bank that is willing to work with you and you will need to complete the full application process for the refinance loan. Many people begin by trying to refinance with the same bank that holds one or more of their existing mortgages, but there is no requirement that you necessarily have to do that- you can apply with any lender that offers mortgage refinance loans.
Qualifying for your refinance will be similar to the process of qualifying for your initial mortgage. You'll need to have your credit checked and your income verified. The major difference is that no bank is going to lend you money to refinance your house unless you have sufficient equity in the house. In other words, the house will need to be worth more than you are trying to borrow on it. If you owe $50,000 on one loan and $20,000 on a second mortgage and the house is worth $300,000, then the bank should be willing to lend you the money. However, if you owe $100,000 on one loan and $50,000 on the other and the house is only worth $100,000, you are probably not going to find a bank that will be willing to work with you on that loan.
Before you decide to refinance a mortgage, you should strongly consider speaking with a lawyer to help you through the process and to look over all the loan paperwork for you.