Although anybody can perform some of the steps in the process, in most states you will require the help of a licensed building professional.
Define the Existing Roof
In order to plan your redesign you have to start by understanding exactly what's in place. Make a rough sketch of your existing roof from the top and sides. Get schematics of the roof's structural components; these are often available from your county records office.
Design the New Roof
Make a rough sketch of what you want the new roof to look like. Based on this sketch and your structural sketch of the existing roof, make detailed notes about what you will need to change in order to bring about the new roof design.
Draw the New Schematic
Based on your notes, draw a schematic blueprint of the structure for the new roof design. You may want to have a professional draftsman or architect complete this stage for you. In many states you will need a professionally drawn plan in order to get your building permit approved.
Get Permits
Apply for your building permit, usually with your county. This process may require professionally drawn plans or an okay from a building professional. It also includes a nominal fee and a waiting period of a week to a few months.
Bid and Build
Unless you're a building professional yourself, contract for the actual roof work with a licensed and bonded roofing company. Get bids from at least three companies and ask for references from each. When calling the references they give you, ask those references for names of other clients who worked with the company. Once you've decided on a building company, don't look for reasons to be dissatisfied; changing builders mid-job is a huge hassle.