To shower with a splint you should cover it with a plastic bag or specialized cast cover and then secure it using some tape or a rubber band.
Wrapping the splint in some plastic wrap or a plastic bag or specialized cast cover will keep the splint dry while you shower.
You can also use Saran wrap and then tape it securely while you shower which will keep the splint dry.
If you can get a splint cover or cast cover you can simply slip the cast cover or splint cover over the splint and then secure it.
To use a plastic bag or wrap you simply place the bag or wrap over the splint and ensure that it's sealed tightly at the top with some tape or rubber band to prevent water from seeping in.
You can also pack the top of the splint with a towel or washcloth before wrapping or sealing the splint to add an extra layer of protection.
Using a handheld shower head if possible can also help to direct the water and make it easier to wash yourself without getting your splint wet.
You can also use a shower chair to make showering easier and more comfortable when wearing a splint.
And taking a quick and shorter shower can also minimize the time the splint is exposed to water.