Colonization, while a practice that destroyed the livelihood of many countries and nations, is an undeniable part of the Victorian era. Paradox intent for it to follow historical parameters in Victoria 3.
To have colonies established, players will first have to have researched the Colonization technology, which is a tier 1 technology that is common to many recognized powers at game start. This will, in turn, unlock Colonization laws as well as the Colonial Affairs Institution, which affects how quickly your colonies will grow.
This means that, if you wish to become a colonial power in Victoria 3, it is unlikely to happen if you're not a recognized power at the game's start.
Players will first need to declare an interest in a certain strategic region, to be able to establish colonies there. In Victoria 3 you will only be able to colonize Decentralized countries, as was the case in actual history.
There is, of course, the route of conquering a region held by an Unrecognized power, but that will likely not be as profitable at the beginning of the game when Decentralized countries are still up for grabs.
Note that having a colony in a state region does not give you a monopoly on it, as other colonial powers can create competing colonies, resulting in split states and messy borders. All of this is likely to create diplomatic tensions in the future as well.