TUSSAM is the official Seville City Buses company, it is quite a good service. You can just pay the driver or if you are going to take a few buses you can get a card to save money, Bonobus, you can buy it at some kiosks or the tobacco shops, it costs 1.5 euros, and then you invest as much money as you want, minimum 7 euros. You can use1 card for 2 or more travelers ticked as many times as you need.
For the city Centre the most useful buses are the circulars, C1, C2, same route different directions and they go in a large circle. The C3, C4, same route different directions and follow the old walls, and the C5, which goes into the centre. You can also get the 13 or the 14. You can find all the routes at http://www.tussam.es/.