The easiest way to memorize a piece is to subdivide it in fragments of four measures long. In each individual fragment you first will master every single measure. This means playing about five times while looking at the score and five times without looking at the score.
Once you can do your measures separately, memorize combinations of two measures The next step is the memorisation of three measures in that fragment. Finally, you will be ready to play from memory the entire four measure fragment without stopping.
Do this for every fragment in your piece and remember to repeat a few times all previously mastered fragments at the beginning of each practice session.
The next step is to combine two fragments into 8 measures, 16 measures, 32 measures, 64 measures and so on. You simply will be making your fragments twice as long. So little by little with every step you will be able to memorize this piece.
Now the question remains whether you will be ready for public performance after that or not? You see although you have already memorized your piece, it takes much deeper practice to be able to perform it in public from memory.
You will need about 100 repetitions of this piece on your own. Remember, at first you memorized a piece but now you have to aim to perfect your piece and progress with it to a whole new level of fluency and play it 100 times from memory.
So unless you can play your piece 100 times from memory without mistakes fluently, you will not be feeling secure during the public performance and performance anxiety will be quite strong in you.
Therefore you have to give yourself an extra time to prepare for public performance. This means you have to be ready at least 30 days before the date of the recital or church service.
This takes careful planning and preparation and keeping track of your goals in your everyday practice but if you want to succeed in memorizing your piece and be ready for public performance and actually perform it fluently in public, then my tips will help you to achieve that.