To change the arrangement of your query tree and which items are shown in it, begin by clicking on the pencil icon at the top right of the tree section.
Give your new View a name (or if you have other views saved, you can select one from the drop-down list to edit it). Most users will only have the option "Save Only for Me" beneath the name box, but administrators can create views that can be shared with other users.
If you want to remove or add nodes to your view, start with Choose Items.
All of the available nodes for whichever module you're using are on this list. You can uncheck nodes to remove ones you don't need to use, or add nodes that weren't selected before. If you've ever used Advanced Search to save a query, the saved query will be one of the available nodes as well.
You can also change the order of the nodes in your tree, and save yourself some scrolling. Click the Set Display Order button just below Choose Items.
In the Text Entries form that opens, you can move a node up or down by selecting it (click in its left margin), and then using the Move Up or Move Down buttons - each click will move it one space.
After you've saved and closed everything, your new view will be one of the options in the drop-down list above the query tree. You can save multiple views for yourself, or choose from one of the pre-designed views.