To build a colony, the barbarian province must be bordered by one of your provinces that has both a) a total population of 10 or more and b) a civ value of 50% or more.
You have to wait for the barbarians in the provinces you wish to colonise to form a horde. You can do this by placing any unit onto the barbarian province. Unfortunately, this can take days, weeks, months or even years to occur. To be honest, I think this is something Paradox need to look into (as they themselves have already commented).
Here's a tip: Recruit 1 unit of mercenary militia and send them to the barbarian province. Have your main army standing by in the neighbouring province. This way, you won't have to worry about attrition or loss of manpower.
The barbarian horde is most likely to march towards the highest civ city (which will likely be yours). There, you can destroy the barbarians on your home turf, with terrain modifiers in your favour.
Once the barbarians have been eliminated, you should be able to click the "Colonise" button on your chosen province. This may not be possible if a) the barbarian army is still present at or marching through the province, b) a neighbouring country has a higher civ province adjecent to your intended colony or c) the barbarian strength is stil too high.
Once you click "Colonise", the colony will begin to build. It will take a few months. I reccommend placing an army on or near the colony. This is because thew colony will still have a barbarian presence in the province and can still rise up. If they capture a new colony, they will reduce it's civ value and burn your colony to the ground, reverting it back into a barbarian province.
Remember to assign the new colony to a trade route. I would reccommend supplying the colony with Grain to help increase the population faster.
Hope this helps!
