There are bus stops all over Maspalomas, including a couple beside Yumbo Centrum. Global runs buses to many of the theme parks. A standard fare within town is €1.40.
If you must take your car down to the beach, there’s a large paying car park beside Playa del Inglés. Street parking costs from €0.50 for 30 minutes, though you will find quite a few streets (along Avenida de Alemania leading to the dunes, for example) where the ticket machines do not work, so you should be able to park for free.
You can call a taxi, otherwise reliable taxi stands abound. From Playa del Inglés, no fare to a destination within the urban area should cost more than €10.