Patching a leaking gutter is an easy do it yourself project that most likely won't take you more than a few minutes and save you a lot of money. Most of the supplies you will need you may have around the house already or can be purchased at any hardware store or building supply.
Step 1 - Determine Where the Leak is
You may have noticed water leaking into your house along the area inside where the ceiling joins the walls. Many times this is due to leaves in the guttering that is causing the water to back up. Eventually this standing water can cause the seams and joints of your gutters to rust then leak, especially along the seams. Clean your gutters completely of leaves and debris so all the standing water can run through to the downspouts. Allow the gutters to dry.
Step 2 - Fixing the Seams
It is easy to fix the leaking, rusted seams where gutters connect to each other. Dry the area with a rag as it must be completely dry for the caulking or roof cement to adhere. Sand away as much of the rust as possible and spray on a rust preventative paint. Apply a bead of the sealing material along the seam and use your finger to smooth it into a straight ribbon. Allow to dry completely. Of course, it is best to do this fix when no rain is predicted for at least 24 hours.
Step 3 - Fixing Holes and Cracks
If you have a large area that isn't a seam that's leaking you will need to follow some of the same procedures as above. Clean away all leaves and water and let dry. Sand the rust with sandpaper and apply a spray on rust preventative. Cut a piece of roof flashing about an inch larger than the hole and lay on a coat of roof patch cement. Stick this over the hole. Once its in place and pushed down, the cement will ooze out around the edges. Use your putty knife and coat the top of the patch with this extra cement. If there isn't enough to cover it well, then use a bit more new cement. Allow the area to dry.
Step 4 - Large Areas
If you have a large area to patch that's damaged or rusted, your best solution may be to cut that section of guttering away with a hacksaw. Then cut a new section slightly larger than the one you removed and adhere it two both sides of the old gutter using roofing cement to hold and seal it.
Step 5 - Copper Gutter
The above solutions are for galvanized gutters. If you happen to have copper gutters the repairs are very different. For small areas and seams that are leaking you will need to re-solder the joint or apply a piece of copper flashing cut to fit the hole and solder it into place. This is good for small fixes. Larger leaking problems are best fixed by a professional who is skilled in working with copper.