If you were going to establish a colony on another world, how would you do it?
Presumably I already have a planet in mind for colonization. It's a planet that has certain natural resources that I think could be profitable, and I want to be able to exploit those resources. I cannot do it alone, and I also know that others will want to get in on this. So my very first step is to create a nonprofit organization (let's call it "The Gloria Corporation," named after my grandmother, who discovered the planet 60 years ago when she used to work for Starfleet).
Me and the rest of my family sit down and put together a business proposal and start looking for people willing to invest in a colony on the planet Gloria. Mostly we're looking for financial support, but in the mean time we're also looking for applications from prospective colonists. Depending on the number of potential applicants we may or may not be screening people for their psychological profiles, fitness, sanity, moral values, criminal history, and overall mental health.
If we do things right, we'll get enough applicants and enough funding to charter a spacecraft that can move a finite number of people and materials to the planet in question. Ideally, we would want the spacecraft crew to be part of the colony, so we would be looking for someone who doesn't have a lot of local attachments and might enjoy some time on the frontier. We would find some way to make it worth his while (he's gonna have a
really nice contract), and compensate him for all of his expenses in the initial setup and possibly the first year or two until the colony is functional.
The people we bring to Gloria will have to be specialists in whatever it is that makes the planet profitable. If, for example, we colonize Gloria because it has huge untapped Pergium deposits, we're going to need miners, engineers and physicists. On the other hand, a planet whose primary export is wild rokeg is probably going to need a lot of farmers, chemists, and somebody who speaks Klingon (actual Klingons would be preferred).
In this example, the ship we chartered for the mission is the SSV Futility, an old freighter commanded by an ex-maquis named Alfred Reynolds who's looking to put the DMZ behind him and start a new life. Futility arrives in orbit of Gloria and we land teams on the surface to evaluate sites for our primary town. We want a place that has access to food and water and with terrain that makes landing and beaming relatively easy. We also want a region of the planet relatively free of large predators or severe weather, and we don't want to be parked in the middle of an earthquake zone. Once we've determined a suitable town site, we also move out and establish secondary sites across the surface of the planet, places where nobody would really live but where workers and/or robots could still do meaningful work (half hour commute by shuttlecraft).
Our chief export from this planet is Trellium-D. It isn't especially valuable, but it's easy to extract which means our operating costs are low; also, it fetches a pretty good price on the black market (inner-city Romulans get hooked on this stuff) and Captain Reynolds knows a guy who knows a guy who can get it past the neutral zone. Our secondary exports include pergium and platinum, both of which can be mined from Gloria's second moon by EVA workers; Captain Reynolds helps us setup a transporter relay so workers can beam back and forth to and from the moon from Gloria City (until it's up and running, Futility's shuttles do twice-daily commuter runs).
For particulars:
I've read modest estimates of between 150 up to 80,000 colonists sent at one time, to establish it.
To ESTABLISH it? That would depend entirely on what the colony is being created to DO. A mining colony would probably start with a few hundred at most, a farming colony might start with a thousand just because of the huge amount of land that has to be cultivated to make it profitable at all. If you're going out there with the intention of building a shipyard for spacecraft heading out to more interesting destinations (harbor town) then you're going to need a huge number of dock workers to manage those ships, plus the construction workers to help build the actual dock, plus the families of both workers, plus shopkeepers and service providers to support those families; that's a starting investment of 3000 to 5000 people, in which case you are almost certainly going to need Starfleet backing from the get-go.
About 1,000 adult colonists should be enough to begin building the colony, I think.
Theoretically, you could start a colony with as few as fifty. A "colony," after all, is just settlement outside of someone's established borders. Provided the town has the resources it needs to sustain itself, all it really needs is a place for workers to live, a place to eat, a place to work, and a place to argue when they disagree with each other. For most colonies, the local bar would probably double as a town hall and main restaurant.
You could establish a central base, then extend 4 outposts (one toward each cardinal direction) toward the horizon, keeping in sight of the central hub and the two adjacent outposts...
Or you could build a bunch of houses on the top of a hill and dig a parking lot for shuttlecraft right next to them. Build what you need when you need it, and not a moment sooner.
Then, as colonists are born and new colonists arrive, you could expand outwardly from that hub.
More likely, they'd be homesteading: find a parcel of land that appeals to you and build a house on it.