Keep anything too hard out of the disposal. The shredder will dull and become less efficient. Small hard objects can also get stuck and jam the rotating parts. Each garbage disposal has its own capacity for hard objects. The more expensive models of the same brand tend to have higher hardness capacities. The instruction manual usually specifies a list of objects to avoid. You can also gain experience with your own garbage disposal. Strong vegetable fibres can jam some garbage disposals, as well. If something may be harder than what the disposal handles, just put it in your trash can or think about setting up a worm composting bin. Some items to avoid are:
Do not put fibrous or starchy items in the disposal. Both can cause particularly stubborn drain blockages (fibers get tangled, and starches get thick). The following items should be put in the disposal in minimal increments, preferably cut into small pieces, or not at all:
corn husk or corn cobs
coffee grounds (in quantity) or coffee filters
fruit pits and hard seeds from things like avocados or peaches
onion skins (unless you're especially careful to completely remove the thin membranes of each, which can wrap around the shredder ring)
egg shells should not be put in the disposal as they turn into a sand-like substance that clogs piping.
All the above are easily composted - see the composting note and link below.
Keep this out of your disposal
Avoid placing trash or hard items down the disposal. Common sense will go a long way, but here are some examples of items to avoid:
plastic or other trash
plant or flower clippings
Cut large items into smaller pieces
If they are too large, like the skins of melons, cut them into smaller pieces and put them one at a time into the disposal instead of trying to shove a large amount in at once. If you find yourself with a lot of larger pieces to cut up, it may be best to place them in the compost or trash instead.
Run water while the disposal runs
Run cold water while the disposal is on. Keep disposer and water running for 30 to 60 seconds AFTER the waste matter has cleared your drain. The waste still has a distance to go. Cold water keeps the motor, bearings and shredder assembly from overheating. It also lets the waste go down easier because the water is pushing it down. Don't use hot water, because it can melt fat and allow it to re-solidify as a blockage further down in the drain.
Clean it regularly With the disposal off, clean the inner side of the rubber in the center of the sink leading to the disposal. It gets very dirty, and gives off an odor when not cleaned. Just wipe it with a paper towel.
Throw some ice down once in a while. While ice will not sharpen the shredders (as is commonly believed) it does knock off any debris buildup on the sharp edges that keeps them from grinding food properly. For better results, make special ice cubes from pure lemon juice or vinegar, or alternate with biodegradable cleanser (label them in your freezer!) Cover and seal ice trays used in your freezer for cleanser, and do not reuse trays for food or drink after having been used for cleanser. While using the disposal, be sure to run cold water at the same time.
Any citrus fruit will do. Dispose orange peels, or any citrus rinds, to freshen the disposal and keep it smelling clean, but cut them into slices first as large pieces of citrus peel, e.g. half a lime, can jam a disposal. You can also use pieces of citrus fruit that may be too old to consume, as long as they're not too spoiled to smell nice. You can freeze these pieces first, if you wish