A hipped (or hip) roof is usually added when a homeowner wants more usable space in an upper area. It is a challenging task, requiring homebuilding expertise, so consult an architect since the change will involve the house structure. It also will require a construction dumpster, a big tarpaulin, lots of help, plenty of time and some money. Before starting, get a rafter table, online or from a building supply store, to help you calculate cut angles for new rafters.
Remove old roofing, decking and framing with a prybar back to the point the hip roof will start, the distance between the end wall and the roof peak. It should be the same as the distance between the peak and the side eaves. If the existing roof is framed with common rafters rather than prefabricated trusses, save them; you may be able to use them (you also may be able to reuse some roof decking). Leave any flooring on the ceiling joists below (if it is a finished floor, cover it with a tarpaulin during construction).
Cut and install three common rafters, one from the roof ridge board to the centre of the outside wall, the other two from the ridge board to the wall corners. Cut notches to fit on the wall cap and extend outside the wall the same length as rafters on the side walls. Nail these in place, making sure they are plumb and straight.
Make "jack" rafters to fit between the diagonal common rafters and the outside walls; you may be able to adapt old rafters for these. Notch them to fit the end caps and extend the same length over the wall as existing rafters. These will decrease in length as you work down the rafter. Start with a jack rafter in the middle of the diagonal rafter and nail them in pairs, one on each side of the roof, 16 inches apart. Then cut and install jack rafters in the centre, parallel to the centre common rafter, from the peak to the end wall. Also, notch these for the wall cap and extend over the end wall.
Deck the new hip roof, either with decking salvaged from the old roof or oriented strand board (OSB). Cut deck pieces to fit tightly together and nail them in place with roofing nails. Nail metal flashings in the valleys where the hip roof meets the old roof and metal drip edge along the eaves. Cover the roof with roofing paper and then nail on shingles; bend shingles at the valley to cover them securely. Cut short 2-by-4 joist extenders to go from the end wall to the end of the extended rafters; nail them to the wall cap and rafters 16 inches apart.
Finish your new hip roof by adding a fascia or facing board on the ends of the rafters and installing a soffit board or cover on the extended roof. This is optional; if the existing roof rafters are open, leave the new hip roof rafters open (or cover all sides with a fascia).
Cover your work area with a big tarpaulin between work sessions. If you are planning a finished room under the new hip roof, consider adding a window dormer for light and more space with little extra work or expense.
Use caution working on a roof.