You have 3 options:
1. Open the song, press the Share button on the top right corner and choose Add to Playlist.
2. Tap on the 3 dots next to the song title and select Add to Playlist. (Available on certain operating systems.)
3. To quickly add multiple songs
Touch the playlist to open it (or create a new playlist then touch its name to open it);
Touch + (icon, top right);
Touch From Library
A window showing your Song library will open, scroll and tap (or search and tap) the songs you wish to add to your playlist. (Songs already in the playlist will not appear in this window.) Any song you tap will disappear from the library window because it has been added to your playlist. A song can only appear once in a Playlist.
Remember to sort your songs alphabetically or manually as necessary
Safety tip: share (export) your playlists individually (in iReal Pro format) to Drive or email (or similar) so you can restore (and they are available if you need to revert to a previous version)