In iTunes 12.2, which supports Apple Music, you can still create your own custom radio station. There are several ways to do it, and you can create a station from the song or the artist.
The Apple reference document I'm using is HT204944, dated June 29, 2015.
1. If a item is already in your library, select the song or the album and look for the three dots (...) to its right. It will look like this for a song
Or it will look like this for an album:
There, depending on the context, you can create your own custom radio station. If it's an album, you'll create a radio station based on the album's artist. If it's a song, you can create a station based on the song itself or the artist.
2. If the song playback is from another source, say, Beats 1, look in the title bar at the top center of iTunes. Again look for the three dots (...) icon to the right of the song. Again, you can create a station based on the song or artist.
These stations will show up in iTunes > Music > Radio under "Recently Played." The stations scroll off to the right as new ones are added from the left, so if you want to see them all, click on the text above the stations that says: "Recently Played." That brings up a page of all stations.
Unfortunately, we haven't yet found a way to delete or reorder the entries there. Right-clicking worked in previous versions of iTunes Radio to delete a station.
Another important thing you can do as you create custom radio stations is to mark the playing song as one well liked, "Play More Like This," or to steer iTunes way from unliked songs "Never Play This Song." Again, these options appear in the three dots (...) popup. Those two options will fine-tune your station's algorithmic selections.
Custom iTunes Radio stations are just another example of how legacy iTunes and Apple Music work together to provide many options and ways of doing things that don't always get discussed amidst the hype of the new features of Apple Music.