The metro is probably the swiftest and easiest way to get around inner areas, and buses or suburban trains to travel a little further out. Buses service the airport and can get you into town pretty efficiently.
Obviously, in a town like Barcelona your boots are made for walking but hiring a bike can be handy too, despite the sometimes hair-raising traffic. Speaking of which, driving in Barcelona is a frustrating business, so utilise the public transport or snag one of the many taxis available if you really need private wheels.
Barcelona's metro system spreads its tentacles around the city in such a way that most places of interest are within a 10-minute walk of a station.
The city transport authority, TMB, runs buses along most city routes every few minutes from 05:00 or 06:30 to 22:00 or 23:00. After 23:00, a reduced network of yellow nitbusos (night buses)runs until 03:00 or 05:00.
Barri Gòtic and surrounding areas are ideal for walking, but you'll probably need to use public transport to reach further-flung sites such as La Sagrada Família and Parc Güell more efficiently.
Barcelona's black-and-yellow taxis are plentiful and reasonably priced.
Bike lanes have been laid out along quite a few main roads and a growing, if ad hoc, network of secondary streets, so it is possible to get around on two wheels.
Citizens of EU countries can enter Spain freely with their national identity card or passport. Non-EU nationals must take their passport.
Spain is a signatory of the Schengen Agreement, as such there are no passport controls at borders between Andorra, Austria, Belgium, Denmark, Finland, France, Germany, Greece, Iceland, Italy, Liechtenstein, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and many of the Eastern European EU members such as the Czech Republic. Think of this zone as one country in terms of your three-month stay. It won't work to try to stay in each of the countries for three months. So if you are planning to stay in Western Europe for longer than three months, make certain that you leave the Schengen zone before your 90 days are up (say by a jaunt to the UK or Ireland) and then return, getting a new entrance stamp in your passport.
Nationals of Australia, Canada, Israel, Japan, New Zealand and the USA need no visa for stays of up to 90 days, but must have a passport valid for the whole visit.
Norwegian, Swiss, Icelandic and EU nationals planning to stay in Spain more than 90 days are supposed to register with the police and obtain a resident's number during their first month in the country.
Those needing a visa must apply in person at the consulate in the country where they are resident. South Africans are among the nationalities that do need a visa. You must obtain the visa in your country of residence. Multiple-entry visas will save you trouble if you plan to leave Spain for Gibraltar and/or Morocco, then re-enter it. Visas are not renewable.
If you have any doubts at all about whether you require a visa or not, or for any clarification regarding entry requirements, contact the Spanish embassy or consulate in the country where you reside before you leave.