Your question is really to vague, it's like asking how are cities established... There is no single mechanism.

You would need to consider multiple aspects:

Are you asking about French, Spanish, British, Portuguese, or another nation as the origin of the colonists?

What time frame are you referring to?

Are you asking about chartered and/or planned colonies, prison colonies, or more organically formed ones?

To get any kind of real answer you need to be more specific.