The table in the upper-left contains the list of "Available" deities. Click on one you qualify for (the name isn't in red italics) and then click on the "Select" button to select it. Once a deity is chosen the Domain table in the upper-right will be populated with the appropriate domains. The number of domains the character can choose and the number of domains they have chosen will be indicated. When you click on a deity the details about it will be displayed in the lower-left window. Likewise, clicking on a domain will cause its details to be displayed in the lower-right window.
There are "sliding dividers" between the deity and domain tables - you can click on this divider and slide it back and forth to your preferred location. There's also a divider between the upper-tables and the info sections below which you can drag up and down to change the viewing area of each. There's another divider between the info sections. This combination of 3 sliding dividers is common to most of the character-related tabs to allow you to change how much screen real-estate is devoted to each section. On most tabs there's a button which has 2 circling arrows that will reverse the orientation of the views between horizontal and vertical. This gives you many options on the layout of the tab.