Well, first up it's not free form. There are rules for what you can and can't do (to a degree). Some things I've left not covered by the rules, others we can decide how we want to play them from a few options.
This is the turn order, so would give you an idea of each persons actions during the turn
1 – Income phase.
Calculate and gather income.
2 – Orders phase.
Order new construction
Order Colonisation of new system
Order movement of fleet assets.
Order trade fleet established.
Order Intelligence operations planned.
3 – Intel Phase
Conduct intelligence actions.
4 – Movement phase.
Fleets move to new location.
5 – Exploration phase.
Supply checks made.
Fleets scan for new system layout and enemy fleets.
6 –Combat phase
7 – Order completion phase.
New technology researched.
8 – Updates phases.
Check for population growth.
Roll Random Event (optional)
Check for Pirate Raids
Check for change in planets Morale
Perform system loyalty check for planets for planets in state of Unrest or Rebellion.
The way I envisioned it playing would be the GM (ie me) would have a master map, the other players would only get maps of what they knew and explored. Systems are laid out on a hex map, with connections between them that speed up travel, but these have to be scanned for and found. You can stay in a system and scan as many turns as you want, and the longer you stay there the more likely it is to find the connections to other systems.
Moving into a new system you'd scan for planets (to see if any are suitable for colonisation), for alien fleets and anything else odd. I haven't got rules for diplomacy, as that would be down to the players. If someone wanted to take the 'kill them all' approach and just wipe out enemy ships, that's fine. If they want to make like Star Trek and seek out new life and new civilisations, then they would simply write those out as the standard operating procedures for their captains and admirals, and I'd interpret those orders when something came up.
There is a tech tree, and lots to research. I may tweak that bit in line with some of the changes I'm envisioning in combat.
Research, construction, fleet maintenance, all comes down to ecomonic points. These are created by your planets, and spent however you like. Unused ones are carried over to the next turn. What you research this turn you can start building next turn, and the bigger things are, the longer they take to build. It might take you 3 turns to build a fleet carrier on your homeworld, and 10 turns to build it on some little colony world.