How do I assign songs into separate playlists?

In the Song Requests sub-tab of your Requests tab, use the platform selector at the top to choose which connected service you're working with, then click the small purple plus icon next to a request — its tooltip reads Add to a playlist — to choose which of your playlists for that platform it should go into. This lets you organize the night — for example, keeping dinner music and dance floor tracks in separate playlists. Multiple playlists per event are available on the Pro plan.