Sextant

To get a sextant you must first of all get the watch. Get each in the following order:

Watch: Speak to Brother Kojo in the in Clock Tower south west of Ardougne's zoo.

Sextant: Speak to Murphy in Port Khazard, located north-east of Yanille.

Navigation chart: Talk to the Observatory Professor and he'll tell you how to use the sextant then will give you a Navigation Chart.