In Saints Row: The Third I own 64% of the 'Deckers' district, but I don't know how to own the remaining 36%.
You gain percentage towards district control from a number of things:
When you hover over a side mission, gang operation, or building/shop, it will indicate how much more control you'll have by completing that activity.
Some activities won't show up until you've finished certain plot missions or earlier levels of that same activity. I think the cribs you unlock at certain points in the plot may also contribute to this percentage, so you'll only be able to get 100% after a certain point in the game.
Each of these also has a small radius that they turn "purple" on your phone's map, so you can tell if you're missing something in an area by checking to see what parts of a district aren't purple. Gang operations don't show up on the map until you've been close to them, so if there's an area that isn't purple in a district and there's not an icon on your map inside of it, go drive around that area and look for a gang operation.
If you manage to get 100% control over a district, you'll get a call from the relevant homie for that district as congratulations, and enemy gang members will no longer spawn there. Owning buildings and shops contributes to your earned income, which rolls over every 15 (real) minutes or so.
You have to do all the side missions, gang ops, own all the shops and buildings, and you have to have done all the activities in the area. All that will make you own all of that territory.
NOTE: The hardest territory to get is the territory that belongs to the morning star which is the biggest territory and most of the activities there are rated hard. You also have to look out for when you are taking over the luchadores territory because they have some of the most advanced weaponry and they have brutes. When you have taken over a territory at 100 percent you will get a phone call and no enemy gang members will spawn and when you have taken over all of the territories you will have no enemy gangs!