You can't.
You conquer a province and send Colonists there until they are colonized and switch to your country.
It's a long process to completely wipe away the Hordes.
If find it's best to work at two provinces at the same time. Send one colonist to two different provinces, that way they can build up residents as the months pass and perhaps save you a Colonist. If the town gets to 900 residents, don't send a Colonist and start on a new one, it'll get to the 1000 needed to switch to you soon and it's better to not waste it (if in the 800's, just send one).
Often, you'll end up fighting multiple hordes and have to deal with them while protecting the provinces being colonized (the enemy can instantly destroy any progress if they get to the province you're colonizing). It's best to just deal with those hordes by conquering one or two provinces and then forcing them to Concede Defeat.
Just hope that Novgorod can deal with Nogai and the Golden Horde (I've been finding that GH has been gobbling up Russian states in v5.1 more frequently)!