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.
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.