Your ship on the galactic plane can move about and little else. Move it onto an 'open' star system and it will jump into the system. Other than that it can nothing else on the galactic plane. If the system is locked out because of lockdown drones then your ship will remain on the galactic map. If your ship would make your fleet out number the points value of other fleets in system by too much then the ship will also fail to jump in.
Once in system a ship can take part in combat - firing drones, manufacturing new units, repairing damage, allocating antibody nano and so on. This is done by selecting the ship - either on the list to the right of the screen, or by clicking on the ship on the system map. Once selected, you can view the ships activity last turn (hit space, or use the mode menu to toggle), or give it orders for this turn. As you give it orders the ship will allocate energy and so on to try to action the orders. If it is not possible a status message is displayed.
The details of how to control your ship are given below:
As you can see, once selected a ships details are displayed. Clicking on the mass scoops towards the bottom of the ships details will power up the mass scoops - the same is true for Spindizzies. Note that mass scoops will also be automatically powered up by the server if your ship has spare capacity. Other than the mass scoops and spindizzies, all control is through the ship outline to the top of the panel. Experiment with right and left clicking upon units and it will be fairly obvious.
Finally, movement and firing of drones is done by clicking on the map. Select the ship to move, and then left click on the map and it will move towards that location. The maximum move distance is restricted by it's design and by the available energy. If the automatic route it has selected is not what you want, then left click on the ship again to cancel the order, and then use the cumulative move.
If you activate the Spindizzies on the ship then the maximum move available will change to be the Spindizzy move rather than the normal engine and mass based moved. You can then set the move as normal - i..e click on the Spindizzies first, and then set the move route.
Cumulative movement is done by pressing 'c' and left clicking on the map. This adds to the existing move path, allowing you to avoid mines and grav wells if you need to.
Firing drones is done by holding down the 'f' key and left clicking on the map (for area effect and mines), or on a target ship for attack drones, or on planets for colonization drones. Alt-f will also entire fire mode, as will the orders menu fire item. You can only fire a single drone at a given target, to cancel a drone order simply hold f down again and click on the same place, then select cancel in the drone window. This will cancel your drone launch order.
You can also right click on the ship to cancel it's drone orders.
Alt-Z will toggle from a zoomed and non zoomed view. In the zoomed view some details are lost, but you will see almost the entire system (depending on your monitor/resolution) at once. This is very handy when planing coordinated attacks.