Great question. Let me see if I can help. This explanation is for the "Reverse" view, which is the default. The "Classic" view will change a few things, but the basic information is the same.
The top line is the text of the NET Bible. When you see a footnote marker there, that links to the footnote contained in the NET Bible for that word. The second line is the Greek text. The number in front of each word indicates the word number in the verse; the database uses that to identify each word. The third line is the Strong's number, which you can click to see the word definition and then the way the NASB and KJV translate the term.
Gray shading indicates that something does not match up in terms of word order. In other words, because of the differences between Greek and English there is either no word in the other language for the highlighted term, or the words are out of order in some fashion.
As you mouse over various words, you can see pop ups which will give additional info, like parsing, Strong's definition, etc.
Clicking on the verse number will open a window which displays essentially the same info, but in table fashion.
Assistant Project Director, NET Bible
Assistant Professor of New Testament Studies, Dallas Theological Seminary