A lot of metal sheds that are built today are not built to last. They are cheaply made of inferior materials, and as a result often leak and look battered and ugly after only a few years. They then need to be disposed of in order to avoid an eyesore on your property. Try to get rid of them through recycling before sending them to the landfill. Even though the shed may be junk, the metal that it's made out of is still useful for other applications.
Give It Away
Give your shed to someone else who can use it if there's any life left in it at all. If you are getting rid of it for aesthetic reasons, there may be someone who could use it in a less visible place, or may not care about how it looks.
Advertise the shed on a giveaway site such as freecycle.org, where people can give and take things they don't need. Take a picture of it and emphasize its good points. People won't be too picky; it's free!
Ask around at local farms or businesses that have large storage yards. People like this will sometimes take free storage space even if it's beat up or ugly.
Take the shed apart into the smallest pieces possible, load it onto a truck, and haul it to your local recycling center.
Contact the recycling center to find out if they'll accept the shed, and to find out if they have any restrictions about the kinds or sizes of metal that they'll accept.
Check with your local municipality to find out if they do a large-item pickup at some point during the year. This could save you the trouble of hauling your shed to the recycling center.
Throw It Out
Take your shed to the landfill as a last resort.
Ask the municipality or the garbage men if they will haul it away. If not, you will need to rent or borrow a truck.
Take your shed to the landfill and be prepared for the possibility of a disposal fee for such a large object.