If you are resident in Greece you will require a residence permit which will also be needed if you want to buy a bike or car. These are issued on Skopelos but the paperwork can be dealt with at the local Police station in Patitiri which is above Taverna Levendis. Go up the stairs to the right of the taverna and the door to the Police station is on the 2nd floor. You will need the following documentation:
Three passport photos cut to size
Depending who deals with the paperwork they will either use their copier/scanner to take copies of your documentation or you may be asked to go to the bank and get a letter to confirm you have a bank account and then go to the KEP office to get your passport and EHIC card verified. The KEP office is located around the corner from the Dimos office on the opposite side of the road, just along from what was Taverna Koutouki
All the paperwork has to be hand written and stamped by the police, so allow at least an hour for the paperwork to be completed.
You will be asked for a date when you arrived in the country which must be within 3 months of the time that you go to sort out your residence permit. You will also be asked for the date that you last left the country. Don't be surprised if they look in your passport for an entry stamp. You will be asked for your parents names and then asked to sign to say that you have the means to support yourself in Greece.
Once the paperwork has been completed it will be sent to Skopelos and will come back to the Police station on Alonissos in about 2 weeks. If you want to get your permit faster, then ask for the papers to be put into an envelope and take it over to the Police station on Skopelos. Their office is along the harbour front to the right above the National Bank of Greece.