You are in Spain. People speak Spanish. But you are also in North Africa, and many people speak Tarifit (Spanish: rifeño, a variety of Berber).
By car (or on foot)
From Morocco. Melilla is completely surrounded by Moroccan territory (and the sea), and this is obviously a very sensitive border. Many try to cross illegally into Spain, with dire consequences. Crossing legally (in either direction) is also an eye-opening experience, but presents no particular difficulties if you are not transporting counterfeit goods or hashish.
Don't forget that Spain and Morocco are in different time zones, so crossing the border into Melilla you will lose one hour, or two hours in summer (Morocco does not observe daylight savings time).
Air Nostrum (Iberia Regional) flies from Málaga (8 flights daily), Madrid (3 flights), and one flight from Almería, Granada, and Barcelona. There is also a helicopter service from Málaga.
There are ferry services run by Acción Trasmediterránea.
Melilla (like Ceuta) is a territorio franco, which means no VAT or other taxes.
Walking into Morocco
Catch a bus from the Plaza de España to the Moroccan border, 2km to the south. Cross the border into the Moroccan customs and security area and line up at the police kiosk to get your passport stamped. This can take a while. Be sure to go up to the window and ask for an entry form to fill out (in French) while you wait.
When you get out you will be in the port of Nador, where you can find banks, a ferry to France, or a bus to downtown Nador. Remember to turn your watch back one or two hours!