Background & Basic Solution:
Android devices (and practically every music player app) can read standard M3U playlist files. So you can just manually copy M3U playlist files between PCs and Android devices. The standard location for Android playlists is the "Playlist" folder either in the top level of your built-in storage or on your SD-card (or both). But I think your phone will typically find your playlists no matter where you store them on your phone.
Elegant, Total Solution with MediaMonkey:
Alternatively, if you use the free media player app
MediaMonkey for Android (MMA) and the free PC media player/manager app
MediaMonkey for Windows (MMW) then you can nicely create & edit playlists on your PC, manage your music collection, and sync your specified music folders & playlists between your devices and your PC (one-way-only, or bidirectionally). MMW is a nice media player which is very similar in its user-interface to Windows Media Player (WMP), but it has more features-- especially around tag-editing. MMA+MMW is a very nice total solution for PC+Android owners,
which I detailed in an earlier post.
One thing worth noting... WMP (I believe still) "syncs playlists" by copying all of the playlist songs into a folder on your phone. I don't really consider that syncing a playlist. MediaMonkey actually syncs the playlist (M3U) file and assumes that you've synced the songs to which the playlist refers. (To me, that's the right way to do it.)
My Current, Simple, Inelegant Solution:
Before I got my Galaxy S5, I used MMW + MMA in order to sync my music and playlists because my old LG phone could not read my WMP M3U playlists, because the file path-names were different between my PC and Android phone. E.g.
C://Users/User_Name/Music/AlbumArtist/Album/Song-name.mp3,
\mnt\music\Album-Artist\Album\Song-name.mp3.)
But my Galaxy S5 can miraculously play my WMP playlists, somehow being smart enough to automatically translate the PC's file-path-names to an Android file-path-names. So now I just manage my music and playlists on my PC in WMP, and periodically I just manually copy and new music or playlists from my PC's Music folder to my GS5's Music folder. And I use the built-in
Samsung "Music" player app on my phone.
Google's Cloud Solution:
You may also want to consider Google's "
Play Music" app. Your music and playlists would be synced through Google's cloud. Relative to WMP or MMW, it's more difficult to create & edit playlists on the PC using Play Music's web-based interface. (That's one major reason that I don't use Play Music. The other reason are that I fear Google degrades my music by transcoding, its a PITA to make your music available offline, and the Play app is always trying to get you to buy Google Music services.)
A Possibly Useful Tool:
Slightly off-topic, but you may alwo want to look at the free app,
Playlist Backup. If your Android device doesn't automatically interpret your PC's M3U playlists (with their PC file-path-names). Playlist Backup has the brains to translate the PC path-names to Android path-names. It can also backup & export your phone's playlists.