I find it easier to learn a new piece, or instrument, when I have the piece I'm trying to play memorized. This makes it so that I can focus on my technique and less on reading the music. We all know that there are different kinds of learners (auditory, visual, kinesthetic). When I started playing piano when I was a toddler, I learned by the Suzuki method, which is by ear. I would listen to the pieces, and learned how to play by ear. If you're a visual learner, take a look at the music and try to find the patterns. For example :
This is a pretty easy piece. Your hands are one octave away from each other, your lowest finger of each hand on C, no black keys, obvious patterns.
If you were to connect the dots between the notes in each hand, you could see that both hands do the exact same thing at the same time. Also note, the first two measures of the first line are the exact same as the first two measures of the second line. These measures are also the exact same as the first two measures on the last line.
If you can see better in color than in shapes (connecting the dots), maybe highlight those three identical two-measure phrases one color. Now, it's clear that they're the same. On the third line, the first two measures and the last two measures are not identical, but very similar. They're the same shape, but they start on different keys. Basically, once you learn the first two, the last two should be a piece of cake.
So, now, you almost have the whole piece, and you really only needed to learn two things. The last two measures of the first, second, and fourth lines are different from each other and aren't part of patters, but they are very similar and related.
If neither connecting dots/seeing shapes, or blocking patterns worked for you, you could always try listening to the piece and trying to match what you hear when you try to play it.
Almost every piece I've learned, I listened to or had heard before. But, after learning it, it goes in my repertoire and I usually don't look at the music ever again. That's because over time, I do learn it kinesthetically, and it's all just muscle memory. I can tell if I made a mistake because I can remember how it's supposed to sound, and I can also see the patterns in my head to help guide me if I get stuck. This is why I think being able to play music is so important, because it incorporates so many different ways of thinking and learning.
If color blocking patterns doesn't work, color each note. Make a Cs one color, Ds another, and so on.
The last way to easily learn a piece is to label every note. Using the piece from above, and noting that the pinky is the fifth finger and the thumb is the first, here's how the right hand would go ..
[ 1 2 3 4 5 5 5 5 5 5 5 3 1 3 2 2 2
1 2 3 4 5 5 5 5 5 5 5 3 5 4 3 2 1 3 1 ] x 2
[ 2 2 2 3 4 3 2 2 2 3 3 3 4 5 4 3 3 3
1 2 3 4 5 5 5 5 5 5 5 3 5 4 3 2 1 3 5 3 1 ]
Because in this piece the left hand and the right hand are doing the same thing, whenever the right hand plays a 1/thumb, the left hand plays a 5/pinky.
Also, on the music, notice how there are curved lines and dots above some notes. The curved lines mean that you want to connect all of those notes smoothly. The dots mean you want to jump off them right after you press them, kind if like the same motion you would make if you were dared to touch a hot stove.
Farewell pic :