The manual says to simply "send a military unit", but that simply does not work!

I just cannot work out how to colonize new planets!

How do you do it?!

I was also confused trying to do this with already habited neutral planets, which I either had to invade or use diplomacy with.

Yeah, the old manual (I still have the paper book lol) didn't do a good job of telling you exactly how certain things work. Suffice to say this part of the game frustrated me at first too.

Note: if you send a troopship to a planet but send troops to the ship after it arrives then you immediately scrap the ship, the troops will be sent to the planet surface (and thus populate it) instead. It's a bug not a feature, and if an enemy fleet arrives at the planet in the meantime your troops will return back to where they came from.