You built this great patio out of bricks but now you find you can't use it as much as you want because of the sun. You need a roof to cover it. How you put a roof over the patio and how much you spend on it will depend with the size and type of the roof and such things as whether it's a permanent roof or a retractable cover.
Get the Size
Calculate the square footage of the roof you'll need, the width by the length to get a base to start your pricing. That will tell you how much material you need, whether you choose fabric, vinyl panels or redwood slats. Determine how much support you'll need, generally a post on each corner and about every eight feet in between, with some rafters or horizontal supports.
You'll also have to decide on a style. Canvas covers, either fixed or retractable, will be cheapest, wood framing with either lattice tops or roof decking with shingles the most expensive. You can probably put up canvas roofing for as little as $300, although you can also spend up to $2,000 or so. A wood-framed roof can cost you less than $1,000 for a lattice top or up to $8,000 or $10,000 if you cover it with metal, fiberglass or shingles.
Look at Kits
If you're handy, look at patio cover kits. You may be able to find aluminum or wood patio covers for between $1,000 and $2,000. These come ready to assemble but you'll have to install them yourself. Prices will vary with the size of your roof; an 8 by 10-foot roof might be less than $1,000, one 20 feet wide close to $2,000. It'll cost you more if you have to hire an installer.
Consider a retractable awning if you only need sun protection for part of the day or year. You can buy most retractable covers for $400 to $1,000, depending on size and whether they're hand-operated or mechanical. These have metal or vinyl frames with canvas covers. Think about maintenance, too. Wood roofs will need painting or staining, canvas will wear out. Aluminum or vinyl are most durable.
Once you've found a style you like, get estimates from several contractors or suppliers. Be flexible. If vinyl posts are half the cost of wood but look the same, make a change. If fiberglass or corrugated vinyl are cheaper than metal, go with the better price that still meets your appearance standards.