As we've said elsewhere, mortgage refinancing is, in reality, not a modification of your existing loan, but rather, the process of taking out a new loan. Thus, mortgage refinancing will essentially be a repeat of the process you went through in taking out your first loan.
First, however, you'll need to decide your reasons for refinancing. Do you want cash to pay for home improvements? If so, you'll need to determine how much money you need. Do you want to increase or reduce your monthly payments? If that's the case, you should figure out exactly how much you can afford to pay. In addition, you'll need to decide what type of loan you want. Fixed rate or adjustable rate? 10, 15, 30-year term or otherwise?
You'll need to make these decisions so that you can have a productive discussion with prospective lenders. Talk to multiple lenders and compare their offers before making your selection. You can use the same lender as you did on your first mortgage, but you do not have to use it. Using the same lender might reduce some of your refinancing fees, but there's no guarantee--particularly if the lender that originated your loan no longer services it.
Once you select a lender, you'll need to go through the loan application process. As you know from taking out your existing loan, you'll need to turn in a vast array of documents, everything from your social security card to old W-2 forms. The lender will then use this information to run a credit report on you and determine its risk in lending you money. The lender will also check on the status of your current mortgage and will likely examine the property via an appraisal, title search, and tax records search. Essentially, the bank wants to make sure you have proven your commitment to repaying the loan.
After the lender has examined your credit report and the current status of both the loan and the property, it will approve or decline your request for a new loan. These approvals or denials can be given over the phone or online, but it never hurts to actually go and meet with your lender.
Assuming your new loan is approved, you'll need to set a closing date and plan your closing with the lender. Find out the size of your closing costs and whether those costs will be rolled into the rest of the loan. If you're not using the same lender as your first mortgage, discuss with both lenders how to make sure your existing loan is paid off. Finally, if other liens (e.g. a small second mortgage) exist on the property, you'll need to contact those lienholders and ask them to sign a subordination agreement. This agreement becomes proof that the small lienholder recognizes the right of your refinanced mortgage over its own claim on the property. Otherwise, this small lien would have priority over the main lender in the event that you default on your loan.