Boats to Capurganá (COP$70,000, 2½ hours) leave daily from the port from 7am. Be sure to arrive by 6am to ensure you can get a ticket, as the boats fill up fast. During high season and at weekends there are often extra boats running this route, but it's still advisable to reserve a day ahead.
There are regular buses to Monteria (COP$44,000, four hours) via Necocli (COP$7000, one hour), where you can connect to services to Cartagena (COP$60,000, five hours). Bear in mind, if you are coming from Cartagena, that it's far quicker and safer to access Capurganá via Necocli and bypass Turbo altogether.
Buses head from Turbo to Medellín hourly from 5am to 10pm (COP$58,000, eight hours). It's possible to reserve boat-bus combo tickets in Capurganá.