The Actual physical buttons and joystick is easy. Dissemble and wipe dry. What can’t be dried can air dried.
The iffy parts are the PCB, the Tubro/guide PCB and the Main PCB.
What you need to do NOW is dissemble your stick, disconnect and remove your PCB, place the PCB in dry, uncooked rice for at least a day, the rice needs to completely cover the PCBs. The inter of the stick can also be packed in dry uncooked rice, but I give it more than 24 hours. Uncooked dry pasta can work if rice is unavailable.
The idea is the rice will absorb all the moister from the stick. You never want to power a device up with water inside.
Only after you allow the rice to do its work for at least 24 hours, only then can you power up your stick to see if it works or not.
The fact that you plugged it in first to see if it worked is a huge mistake. As the water can short out the stick and potentially ruin the PCB.
Next time you spill water on anything electronic, unplug it (if it isn’t already) wipe dry and pack in dry uncooked rice for 1 to 3 days. Something more complex like a laptop you want to give 3 days to dry completely, unplugging the laptop and removing the battery first.
If the PCB is bad the stick can still be repaired with a PCB replacement.