How to make an Apple Music playlist in iTunes or on iOS
On iOS
To create a new playlist on your iPhone or iPad, tap the "My Music" tab on the bottom menu bar, and then the Playlist tab near the top of the screen. That will show your recently added playlists on top, and all of your playlists below. Under "All Playlists," tap "New." The font is tiny, so check out the screenshot to the right for a visual.
Name your playlist and customize it with a photo and a description. Then tap Done. If you try to add songs to a playlist before you're done creating the playlist, you won't be able to. Save yourself some frustration. (And forget about trying to add a song to a playlist you're creating on the fly, like you can with Spotify's app.)
Did you tap Done yet OK, stay in your playlist and tap Edit, then Add Songs. Apple lets you create playlists from music you own as well as its streaming catalog, which is one of the service's big selling points--rivals like Spotify and Rdio don't do that. To add songs to a playlist from music in your library, you can use the search bar (just make sure you toggle over to My Music instead of searching all of Apple Music), or comb through your collection manually. Tap the + sign next to any of the song or album titles from your collection to add it to a playlist. Apple Music doesn't give an obvious confirmation that a song has been added, just a tiny notification at the top of your screen, but don't keep tapping that + sign--you'll find you just added the same song 10 times. (I may or may not be speaking from personal experience.)
To comb through Apple Music's catalog, tap Apple Music and enter the song, artist name, or album title you're looking for. Once you find the tune you want to add, tap the ellipsis, or the three dots to the right of the song title. That will bring up a new menu of options like Play Next, Add to My Music, and Make Available Offline. At the bottom of the menu is Add to a Playlist. Tap that, then pick which playlist you want to add it to. You can keep hunting for songs and add them to your playlist, or you can stop and tap Done to wrap it up for the time being.
If you want to add songs to that playlist down the line, just tap the ellipsis next any song title to bring up the menu--Add to a Playlist is always at the bottom.
In iTunes
We all know the way iTunes organizes and displays your music library is best described as a "hot mess," and Apple Music only made that more complicated. To make a new playlist, click on Playlists on your top menu bar. Then click the + at the lower lefthand corner beneath your list of playlists. Name your playlist and add a photo and description if you want. From here you can drag and drop songs from your Apple Music library--both songs you own and songs you've added to your Apple Music catalog--into the playlist, which is much easier than the rampant use of the three-dot menu in the iOS version of the app.
But to add songs to a playlist that aren't in your Apple Music library, you'll have to use the search bar. And unlike Spotify, which lets you drag and drop song titles from the search bar into a playlist, Apple Music rips you out of your playlist and throws you into a page of search results, where you have to use the ellipsis (yes, it strikes again) to add the song you want to your playlist.
This is where it gets a little strange. Sometimes Apple Music will let me add a song to a playlist immediately when I open the menu behind the ellipsis. "Add to" will be an option right away. But other times, it forces me to add the song to My Music before it will show me the "Add to" option, which means I have to click two extra times to add a song. It's a mild annoyance, but still not the seamless user experience that Apple could offer here.
The fact that it takes so many steps to add music to playlists in Apple Music sums up one of the service's biggest problems: It is too complex, and buries what should be its most basic features behind layers of options. If Apple can't simplify Apple Music, it will lose subscribers to services that aren't trying to do it all.