It’s easy to shuffle a For You playlist—each one has a Shuffle button right at the top. Or you can tap any song to begin the playlist at that point and play the rest in order. But if you want to tweak the order to your exact liking, or even ditch a song before it plays, just start the playlist going and then tap the mini player, and the Up Next button. Then you can drag the songs into a new order by pressing the hamburger button (three lines in a stack) and dragging them up or down, or swipe right-to-left on a song you don’t want to hear and tap Remove.
Note that this doesn’t alter the playlist permanently. If you’ve saved it to your library, it’ll still appear in its original order, with all the songs present. If the curator changes it later, it’ll update in your collection automatically, but I wish Apple let me duplicate a curated playlist so I can add, remove, and reorder songs and save it as as a personalized new soundtrack.