Simply drag the songs into the Playlist.
The easiest way to do this is to have the Playlists showing in the sidebar, on the left and then drag the songs from the Songs View. If the Sidebar is not currently displayed in your iTunes, click on View/Show Sidebar:

Once you have the Sidebar displayed, use the Songs View to find the songs and then drag them into the Playlist. Note that the Playlist needs to be a Regular Playlist, not a Smart Playlist or a Playlist Folder:

If you have created a Smart Playlist, or a Playlist Folder by mistake, delete it and use File/New/Playlist to create a regular one.
Once you have your Playlists ready, if you Sync all your music to the iPod, simply let a Sync take place. If you Manually Manage, you need to drag the Playlist onto the iPod from your Library. using Sync is much easier in the long run.