With Hat Yai as the major transportation hub of the deep south, Songkhla province is extremely easy to get around. From Hat Yai, buses and vans fan out to all points, including neighboring provinces. The best place to get a ride to most points in the province is in front of the old Plaza Cinema on Petchkasem Road. From here, vans leave as soon as they're full to Songkhla town and Sadao on the Malaysian border.
Several guide books talk about 'shared taxis' that can be picked up around Hat Yai town. These don't really exist any more. They've been replaced by air conditioned vans which leave from several places around town, although most of them stop at the Plaza Cinema on their way out of town. This is the best place to get a van, since most of them are not marked in English. At the Plaza Cinema bus stop there are usually at least one or two 'conductors' who can point you to the right bus.
For getting around both Hat Yai and Songkhla town, there are four-wheeled tuk-tuks as well as motorcycles. It usually costs no more than 10 Baht to go anywhere. There are metered taxis as well, but I've only seen one or two around town.