Much of Seville is quite walkable, especially the historic city with its narrow streets and closely knit shops and cafes.  The Triana section of the city, also older when compared to the city's most modern section, is very pedestrian friendly as well and has a lot to see by foot.  For getting around other sections of Seville, the city has plenty of available taxi cabs and a well run public bus system.  Getting around by taxi or bus is recommended if you have a specific destination in mind and do not wish to walk. For buses Tussam has a very good bus map available from the information offices with all the routes or see Tussam's site http://www.tussam.es/ that shows routes and maps. The most useful for the city centre are C1 to C5 that go in a circular route around the centre. The bus fare is 1.10 euros (Oct 08) that you can pay on board or you can buy a book of 10 tickets (bonobus) for 5 euros that you buy from kiosks in the street with prensa written on them.

There are also bicycles available on a 'self  service' basis at various locations dotted throughout the city called Sevici see http://www.sevici.es/ which the locals use a lot but all the information is only in Spanish so it is a little dificult for foreigners. It seems you need to subscibe for at least 7 days that costs 10 euros and then you pay for the time you use. The first 30 minutes are free, then you pay 1 euro an hour for the first hour and 2 euros the second. The idea seems to be to use them t get from A to B but you need to know where the 'bicycle parks' are before you set off. If you're there for a longish time ad enjoy cycling it would be worth investigating.

As well as any of the good tourist maps, take a cheap compass. There are many short, narrow, alleys, and a compass makes navigation far easier.