1) you can, and probably should, talk to your neighbor about it. He might be able to move the structure, or you might come to some alternate arrangement. Resolving any disputes out of court can save both of you legal fees, as well as the stress of hiring lawyers and going to court. If you and your neighbor decide to leave the encroachment in place, you may consider giving them written permission to use your property. This can prevent a later claim of adverse possession.
2) Alternately if the neighbour is willing to pay a price for the portion of the land he wants to use and you are willing to sell you may do so.
3) Legal option is to file a suit demanding the demolition and vacation of the neighbour. It is difficult to predict how long it will take and if they can prove in court that they have been using your land in this manner for quite a length of time they can manage a verdict in their favour as well. The litigation can go on for years.You will need to prove in court your ownership and the improper and illegal use by the neighbour.