What are some good study tips to help me remember the Bible?

I'm glad to hear you're wanting to memorize scripture. This will help you in so many ways, not just in helping other people. There are many ways to memorize scripture. I'll give you a few ideas here and you can see what works best for you.

I use a notebook when I study/read my Bible and I write down thoughts, questions and verses I want to memorize. Sometimes I use a dry erase marker to write a verse on my bathroom mirror (I read it every time I wash my hands.), on my refrigerator (This only works on smooth refrigerators.), on the tile backsplash above my kitchen sink, or on the whiteboard over my desk. You could also write a verse on a piece of paper to hang/stick where you will see it and read it often.

I think one of the best ways to memorize scripture is to use 3x5 index cards. Most people I know use white index cards with pencil, blue ink or black ink. But by using either colored pens or colored cards you could divide your verses into sections. Red ink on a white card for salvation verses. Yellow cards for praise verses. Purple cards or ink for encouragement or joy verses. Green for prayer. Blue for Christian life. Pink for women. There are so many ways you can use color to help you memorize scripture.

I like to write the Bible reference on the front, blank side of the card. Then on the back, lined side of the card I write the verse, breaking it up into phrases. For example, I would write Proverbs 16:24Pleasant words are as an honeycomb, sweet to the soul, and health to the bones.
See All... on the front of the card, and on the back:

"Pleasant words are as an honeycomb, sweet to the soul, and health to the bones."

This breaks the verse up into smaller portions which makes it easier to memorize. Read the reference, then the verse, then repeat the reference. The first word is the most important. So, just say "Proverbs 16:24Pleasant words are as an honeycomb, sweet to the soul, and health to the bones.
See All......Pleasant." several times to get started. Once you have the reference without a problem, it's time to work on the verse. Read it slowly several times, then read through it several times as fast as you can. Carry it in your pocket and work on it whenever you have a few minutes.

You might also write the verse on a piece of paper. Read it three times. Mark out one or two words. Read it three times. Mark out one or two more words. Keep going until you have marked out all the words and can say the verse.

Start with only three to five verses. You can add more as you come to know these by heart.