Welcome to BYC.
That's a great score to use as a foundation for your build.
Here is some basic information for you to consider as you work with it:
The Usual Guidelines
For each adult, standard-sized hen you need:
- 4 square feet in the coop (.37 square meters)
 
- 10 square feet in the run (.93 square meters),
 
- 1 linear foot of roost (.3 meters),
 
- 1/4 of a nest box,
 
- And 1 square foot (.09 square meters) of permanent, 24/7/365 ventilation, preferably located over the birds' heads when they're sitting on the roost.
 
https://www.backyardchickens.com/articles/repecka-illustrates-coop-ventilation.77659/
	
		
	
	
		
		
			a coop and run for 4-6 chickens this spring.
		
		
	 
4 hens
- 16 square feet in the coop. 4'x4' is the only really practical build for this given the common dimensions of lumber.
 
- 4 feet of roost
 
- 40 square feet in the run. 4'x10' or 5'x8'. 6'x6' is a bit too small, 6'x8' is more generous and easier to build than 5'x8'.
 
- 4 square feet of ventilation. A 2'x2' window is theoretically enough, but in practice doesn't create any air FLOW so better to spread the venting around (and even better to exceed the minimums, especially in warm climates).
 
- 2 nest boxes, to give the hens a choice
 
6 hens
- 24 square feet in the coop. 4'x6' is the only really practical build for this given the common dimensions of lumber. If you can't walk into it, put the access door in the middle of the long side to make sure you can reach all areas of the coop because a stubborn chicken WILL press itself into/lay an egg in the back corner where you can't reach.
 
- 6 feet of roost
 
- 60 square feet in the run. 6'x10' or 8'x8'.
 
- 6 square feet of ventilation.
 
- 2 nest boxes, to give the hens a choice
 
	
		
	
	
		
		
			The dimensions are 7’8” by 4’8” and 6’10” tall.
		
		
	 
So you have roughly 34 square feet -- room for up to 8 adults. Lovely! Having extra space is very helpful because it gives you room to move around, to have some equipment, to add some 
"clutter", etc.
Even more importantly, when you get severe winter weather so that the chickens either cannot go into their run or don't want to they still have some space to keep out of each other's way and not get on each others' nerves.
What's your level of DIY skill?
Regardless, one of you best options will be to take the plywood panel off the top and install the roof, extend the corner posts above the current sides, and use that area under the roof as your main ventilation.
A shed roof would be the easiest to build, but if blowing snow is a problem then a gable roof would better protect the roof-level vents. Vent either one with open soffits (covered with hardware cloth), and wire at the tops of the long wall.
Add additional vents at the top of a gable roof with commercial ridge vent and/or open triangles covered with hardware cloth at the gable peaks.
Regardless of roof style, leave a generous overhang all the way around to keep weather out of the vents. Create even more overhang on the nestbox side so that you don't have to stand there with rain dripping on your head when you're collecting the eggs. 
