I press A when standing by a river and the lily pad forms on land, I get on but still can't cross. Am I supposed to toss it into the water? Since u can only use it once a day I haven't been able to experiment with it much and I really have no idea how to use it
You can't enter the river at any point. Only points that descend into the river. It's like needing to use stairs to go down a floor.
In Vale River, there's a sign post to the right of the save point near the entrance, that mentions how you can't walk on the river. Right next to that signpost is where you can enter the river on your lilypad.
And the lilypad lasts for as long as you don't put it back into your rucksack. So if you want to try it somewhere else, just pick it up and run there.