There are places on the pier/dock where you can activate it. It's sort of like the jet ski icon but for the floats. There are actually 4 or 5 locations if I'm not mistaken.
Is this the private space or can you use it on the public beach as well?
There is one activation in the private and multiple ones in the public. Guests don't need the float but if you want to do it by yourself you need one of them. I was at the beach all day today.
There is a free reward for being a guest. The headband and it's not region locked. My Japan account got the reward this evening and I had someone from the EU get it earlier today.
Locations are here.