A friend of ours was taking down some old fence and was going to use it for firewood. Instead, we got to put around our backyard. Here is how we did it.

Need:

Old fence
post hole driller (can rent or borrow)
quickcrete
pea gravel
drill and screws. I used torx screws.
jigsaw or reciprocating saw.
green treated 4x4 posts meant for sub-ground use
rope line and stakes
level
bricks

Since we got the salvage fence free the total cost was from the green-treated posts ($8 each - 10), quickcrete ($4 per bag - 8 bags), gravel ($10 - 1 bag), screws (~$5)

Step 1: Materials

Prepare your materials. Rent or borrow a post hole driller. We used a gas one which starts like a lawn mower and is not too difficult to use.
We used 8 bags of quickcrete for 10 holes, 1 bag of gravel for all 10 holes.
We had to spend a couple of hours removing the old nails from the fence sections that we reclaimed. I use an old cat litter container for old nails and screws and such. (We did the nail removal while we were waiting for the quickcrete to set after the next step)

Step 2: Holes and Posts

Stake out the line for your fence and stretch a rope line along it so that the line is straight. Then measure the fence sections and mark where the holes need to be with flags or stakes.
Lay out a bag of quickcrete and a green treated post beside each hole.
Drill each hole 2 feet deep (1/3 the height of the fence)
Pour about 2 inches of gravel at the bottom of each hole, tap it down with a post
Insert a post into each hole and pour quickcrete around it about half full, then adjust the post so that it is vertical using the level.
Spray some water into the hole to start setting the quickcrete
Fill the rest of the hole with quickcrete and then pour water on the top to set the top quickcrete.
Move to the next hole and repeat until all of the posts are up.

Step 3: Hanging the Fence

Wait about an hour for the quickcrete to set before hanging the fence.
Place bricks or some other spacer on the ground along the rope line so that you can rest the fence sections on them. This will raise the fence a bit above the ground and hold it in place while you work.
Now hang the fence sections by drilling and screwing into the green-treated posts. You will have to decide which side of the fence you want the posts. Since this is a backyard we decided to have the posts along the outside of the fence so that the fence looks continuous from inside the yard where the people are. If we were fencing the front yard we would have chosen to have the fence posts inside the yard so that it looks better from the street.

Step 4: Finishing

Once the fence sections are up remove the bricks, use a saw to cut the tops of the posts and the tops of the fence sections if you need to so that everything is level.
Cut the tops of the fence posts at a 45 degree angle outward, away from the fence, so that water will run off the top of the fence post and not collect on it.

We then planted grass, set up yard furniture, planted vines, clematis, and climbing rose bushes, and hung old window frames and picket fence pieces on the fence so that the climbing planets have something to climb on. It is already looking very cosy!