If you learn your songs from tabs or standard notation, you might be struggling with learning them by heart. I remember that when I was beginning, my sight reading was so poor that I had no other choice but to memorize the material. What I see in my students (especially playing easier pieces) is that they keep on reading from the paper no matter what. The way I try to get around that is to make them learn and practice a song bar by bar. And it’s much easier to memorize it that way.
When you take up a new song you probably play through it couple of times. Oftentimes that’s how people keep practising – just playing the whole thing in a rugged way and hoping that it gets better. Practising smaller beats is much more effective but the quickest way to learn the song and to free yourself from the tyranny of paper is to make the bit you work on as short as possible. Learn just one bar (two at the most). Practice it without looking at the notes until it flows. Than practice next bar the same way. Then join them etc… Practice that way until you complete a single phrase. Than play this phrase over and over again until you don’t have to think about correct notes or fingers.
The funny thing is you have to do this work either way. But by doing those small bits by heart you’ll end up with well practised and memorized song. If you put the memorization work in from the beginning you’ll barely notice it. The alternative is you can learn the whole thing from the notes and only than start memorizing it. But than you’ll have a lot of unpleasant work to do.
If you practice with the notes in front of you, the temptation of looking at them might be too strong. Consider putting the notes at the other side of the room so that you have to get up every time you forget what you have to play. That way you’ll have much more motivation to remember what’s next. Also whenever you struggle to remember something, when you finally do it on your own it’s written much better into your brain. On the other hand, if you just look at the paper, the brain learns that it doesn’t have to remember because the paper is available. So once you read the piece you want to practice, use the notes only as a last resort.