Define your purpose behind refinancing - whether you want to change the interest payments, or shift from an adjustable rate mortgage to a fixed one, or simply want to make low monthly payments.
This will enable you to build your case. As your credit history is already under scrutiny, you will need to assure the lender that you will not default, and for this reason, you will need to outline the purpose.
Determine the equity in your home. It is basically the difference between the value of the home and the mortgage held against it. Having equity at your disposal will give you suitable options when it comes to refinancing. It will further assure lenders that you will not default on your payments.
Contact your current mortgage lender. This will be your starting point, as you have already established a relationship and it may come to your advantage, and the existing lender may help you out.
However, it is also important that you research all possible options before picking your desired lender. Most companies specialize in home equity refinancing, and might offer you a better deal. Search the web, and compare the rates on offer in your area. However, the disadvantage of choosing a new lender is that you will have to start the process all over again, where you will be gathering all necessary documentation. Also there will be other mortgage related fees which you may need to pay upfront, if the lender does not include them in the new loan agreement.
Now choose the lender and pick the loan type which best suits your need. This will again depend on your long or short term aspirations. If you intend to stay in the house for long, then you may look for fixed payments.
Complete the paperwork and sign the agreement. At this moment, it may be necessary to get a new home appraisal before the refinancing process can be completed.