You have 3 options:
1. Open the song, press the Share button on the top right corner and choose Add to Playlist.

2. In the main song list, swipe a song title to the right and choose Add to Playlist

3. To quickly add multiple songs
Tap the playlist to open it (or create a new playlist then tap its name to open it);
Tap + (icon, bottom left);
Tap 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.
When finished, tap Done.
Remember to sort your songs alphabetically or manually as necessary

Safety tip: share (export) your playlists individually (in iReal Pro format) to Files or email (or similar) so you can restore if necessary (and they are available if you need to revert to a previous version)