First with the memorization, even if you can read music having the tune in your head is important,, especially if you are attempting to play any traditional music.
I have a few sheets of music on my stand, new tunes I want to learn, with audio reference for reminder. After a warm up of tunes I enjoy, I play through the new tunes a few times each, working to the point of eventually being able to play with only the title for reminder. I don't usually labor over tunes until I can play them free of the dots. This usually takes about a week, the tunes I am less fond of either take another week or get dropped.
After the tunes have been played a few times each, I go back to playing tunes I know and love. The actual practicing of new tunes is probably less than 20 minutes of my hour or so of playing. It is important to end practice time playing well so you go away feeling good about your music
After I can play the tune easily, then I fill out the tune by working on fingering, which I usually don't do much changing now, with 25 years of Anglo concertina playing, and any ornamenting or doubling, what I want to do to make the tune mine.
For me, the final step is pairing the tune with another tune or two to make a set so that it gets played regularly. A tune left on its own doesn't get played as much, and thus is forgotten.
Mike