You read it in context.
You read it over and over again in different translations (using other Bibles or a parallel Bible).
You define words with a dictionary, Strong's Exhaustive Concordance and/or Vine's Expository Dictionary. (Of course, you need to know how to use Strong's and Vine's, it's not too hard, but you may need some instruction.)
You read what a commentary has to say about that verse.
You diagram and draw, doodle, highlight, underline, etc.
You personalize the verse. Re-write it in your own words.
Think of how you can apply it to your life.
Meditate on it and journal what comes to mind.
Jot down further questions.
As you get to know the Bible better, write down other scriptures that come to mind and that help you further understand this verse.
You could write a prayer using the verse.
Mapping a verse is a way to break it down in manageable pieces and then rebuild it as you understand it. You will begin with a little brainstorming (with God, of course), move on to research, and end with application and prayer.
There is no cut and dry technique, no right or wrong way. Use your imagination and fit it to your own style. I like to draw but you may not be comfortable with drawing. Diagramming will be done in a way that makes sense to you. You can highlight, circle, underline, use symbols, or all of the above. Whatever comes natural to you. If you don't have the study aids (Bibles in different translations, or a parallel Bible, Strong's Vine's, Bible dictionary), then look online. There are free software programs for Bible study, apps, websites that have these things. You may use sticky notes of one type of another, index cards, sketch pad or blank notebook. It's up to you.
You can do it by hand or digitally. I'm pretty proficient in using Adobe Photoshop Elements for digital scrapbooking so I can do mine as if I were doing a digital scrapbook page (see my examples below). I still like to draw a cartoon at times. When I do that, I'll scan it in and save it as a .jpg file and insert as an element.
You might like to use colored pencils or highlighters, colored markers, pens, pencils, washi tape, stickers. It's up to you how decorative. Of course, the main purpose is not a journal art page. The main purpose is studying scripture. So don't get bogged down in decoration. Keep your focus.
If you are new to Bible study, your verse mapping may be more simplistic. As you get to know the Bible and mature spiritually, verse mapping can become more involved. More things come to mind, other scriptures pop up, etc.
Begin every Bible study with prayer, then select a verse and go to it. You will settle into your own style.
Here are my examples:
You can Google "verse mapping" and see many more examples to give you ideas. I will include some other examples that I found doing a Google image search. They inspired me and I appreciate all those who share in order to inspire us in this method of Bible study.
As you can see, you can be as artistic as you wish. But if you aren't, then stick to highlighting and diagramming along with your research. Once you feel like you understand the scripture, it's time to meditate on how to apply the Word you have learned to your own life. As you prayed before you started, it is time to pray and ask God to help you apply the Word and to be thankful for what He has taught you during your Bible study time.
There are many other Bible study methods and I hope to do some further investigation on it.