I know I shouldn't drink seawater (because of the salt it contains), but how can I desalinate it?
You need to distill it - I'm assuming that freezing is not an option (unless you're camping in the extreme latitudes). This is easiest, as the ice on top is almost pure water.
Where you don't have a freezer available - boiling the water, capturing the steam and condensing it back to water will provide pure water.
Outdoors you can dig a hole and build SOLAR STILL. It is quick and dirty but works very well and it is time tested.
Or you can put big plastic bag over brach with a lot of leaves on it and put rock on the bottom to capture the water. Make sure you don't do it on foliage that is toxic to people.
If you have the bucks you could get a portable Reverse osmosis filter.
Electrolysis turns the salt water into oxygen and hydrogen then recombine them and the result is pure water.