First, you need to develop your colony to the point where you can produce water, oxygen and energy - these are the three main resources you need to create a functional dome as well as living quarters for the colonists. In addition, you will need metals and polymers to build the dome itself. All this must be collected before the dome is ready to receive people.
Create buildings that generate electricity, such as solar panels and windmills, and use power lines to control the power in the dome.
Then create a moisture vaporizer to extract water from the atmosphere. If you start the base game, you usually get one vaporizer to build your first dome and launch it. As with power, you will need to run a line (pipes this time) from the water-generating sources to your dome.
Finally, do the same with oxygen. Create a couple of MOXIE buildings and blow oxygen through the pipes to the dome. Oxygen is a little easier to obtain as you can easily build MOXIE without the need for any prefabricated buildings or natural resources.
Once your dome is finally set up and you have living quarters and some kind of food production mechanism, you can start preparing to host colonists.
Click on the rocket in the lower left corner (denoted by the rocket symbol) and select the launch of the passenger rocket. From there, you can choose which candidates you want to hire and then view all the people who are applying to live in your colony. Choose as many as you can populate and then choose to launch the rocket. You need to wait a bit. Once the progress reaches 100%, you can click it and choose where you want to land the rocket. You don't need to place the rocket right away, but keep in mind that there is a time limit and if you don't place it before that time, the colonists will die.
Place the rocket within walking distance of your dome (the game will tell you if you chose the correct distance) and if all goes well they should move on to your dome and start a new life as colonists. If something is wrong, the game will inform you that you need to urgently fix it, otherwise they will die.
