How to play

Begin a new game

have a look to to do list#Features Overview, especially to columns like SinglePlayer or MultiPlayer.

see Start Game Panel (for options like Galaxy size or Tech Level)

control food - avoid starvation (so build farms just in time!)
control labor pool and assign it
sometimes control structures if they are online
maybe make individual research assignments
check everytime your ships to avoid wasting their time
for expanding range maybe build a construction ship which can build an outpost
check everytime that your shipyards are running
check everytime your building queues: one turn left is too less, better 2 or 3 turn left (to avoid waste of industry)
in MP: try to build shipyards as soon as possible to increase ships

F1 (it's Galaxy Panel) -> and then click on "Turn" (left top side) to finish a turn
F2 System Panel: Production - Structures - Build List - ShipBuilding
F3 Embassy Panel: Overview - Agreements - Inbox - Outbox
F4 Science Panel: Research Matrix - Encyclopedia
F5 Intel Panel: Colonies - Agents
right mouse -> Pop-up Panel Access Menu

to control your systems (labors and shipyards) just use arrow keys left and right to switch between the colonies
- first click left or right will bring you to back to PRODUCTION
- next click left or right changes the system
  - doesn't work if you select the system via dropdown list
    - to bring this function back to work just go to galaxy map and jump with double clicking a sector into one system -> than left/right does work again

it seems to be important to search for systems with dilithium and raw material. Systems with many moons are good for the building Moon Habitation
with transport ships it might be available to conquer systems (don't know exactly)
Empire's insignia top right shows at mouse over which human player has which race