You will most often be looking at the galaxy and the systems. At the very top (1) you choose between normal and economy view, which will come in handy later. In the upper left corner (2) there is a small status window, that keeps you up to date about the state of the treasury and Dust income every turn, as well as the status of Influence points and their income. You can also see which technology is currently being developed and the state of strategic resources in stock. At the top of this panel, there are shortcuts to the various screens described below. If you hover over the name of a system with the cursor, in the lower left corner you will see a brief summary (3) of that system, its FIDSI revenue, population status, etc. (works similarly if you hover the cursor over a fleet). When you select a fleet (or ships in a hangar) you will see its status at the bottom (4) and all possible actions you may take, such as upgrading or assigning a hero. In the lower right corner (5) there is the turn end button (and the turn number). Above it, there is a button which selects fleets that do not have any orders, a button which continues the movement of fleets (the ones which have longer routes planned out) and the options button. The right side of the screen also contains icons for notifications and events.
In the game you will find many useful tabs/screens, which will help you to effectively manage your galactic empire. This will make it easier for you to find the information you need, such as the support for an ideology, or to show which system generates the most revenue and where you need to make some corrections. You will be able to check the progress you have made regarding a specific victory condition or what technology you need for the next stage of development. Below you will find the descriptions of each of these aids.