OK, you said you just want it to be weathertite for as little money as possible and you're not to worried about how it looks. Time is also money, so we don't want to make it too complicated.
First, I'd get a roll of house wrap, and wrap it all the way around the sides of the building. It's probaby not tall enough to make it on the peaks, so don't worry about it, Just be sure to get a good overlap of at least a foot with two feet being better. Staple it on with a roofing stapler. Then cut a piece off that is several feet wider on either side than what you have left to cover at the peak. Overlap this over the first layer by several feet and drape it over the roof. Staple it all down on the sides and onto the roof. It should be done so that water running down the side will go all the way down the wall without getting under the house wrap.
You should have some of the house wrap going up onto the roof all the way around. That should also be stapled to the roof before you do anything else. There should be no loose pieces that are not stapled down.
At the door, cut a big "X" and fold the ends into the building along the door jams. To do it right, the door should have been removed, but I sort of think there is no real door fram, just a hole cut into the wall. Wrap the fabrick around and into the building. Staple it down.
To cover the sides and make it last, the cheapest material you will find right now is OSB siding. Some people don't like the way it looks, but that's up to you. More money will give you more options, but this will work and it will last for decades. Nail or screw it on to all your walls all the way up to the roofline.
Now you need to flash the edge of the roof where it meats the walls. There are several types of flashing to choose from, but the cheapest and simpliest is just a simple "L" shaped flashing. Put it on over the top edge of the OSB and attache it to the roof with Galvanized nails or tacks. The idea is that water will not be able to get behind the OSB or even on top of it. Water will come into contact with the flashing and then run down the outside of the OSB.
Overlap your corners with the lowest parts going on first. You always want to overlap with the highest points going on top of the lowest ones.
The cheapest and easiest roof is gonna be asphalt shingles over tar paper. The cheapest stuff will work fine for this. Unroll the tar papar and staple it down from the lowest point first. Cut the ends off to be even with the flashing after you staple it down. Then overlap it a the lines on the paper. Do this until you get to the peak. Then do the other side until you get to the peak. At the peak, overlap both sides and staple it down.
Rembember that the tar paper is what keeps the water out. It must have total coverage and it must overlap itself so that water will run downhill and off of the building.
To protect the tar paper, you put on the shingles. First row is done backwards at the very bottom. Turn the shingle so the tabs are faceing up and the top, straight edge is at the edge of the roof and overlaping your flashing just a bit. Nail this one down on the lines on the shingle. Always nail on the lines. Three nails per shingle is good. You don't need a nail gun for this as it's such a small job. The next run will go right over the top of that backwards one, but now the tabs are facking downwards. Overlap your seams and nail it down on the lines. Work your way up to the peak, then do the other side the same way.
To do the peak, you need to cut your shingles at the tabs. Look at the shingle and see the space between the tabs. Cut there to the back of the shingle to make each tab it's own shingle. DO NOT cut off the tabs, but make sure you cut the entire shingle into three smaller shingles. This is if you bought three tab shingles.
Start at one end and fold the shingle over the peak so the tap end is facing out. Overlap each tab and work your way to the center of the peak. Stop and do the same thing from the other side. At the middle, just overlap both ends to tie them together.
It will take awhile for the sun to relax the shingles and let them lay flat. Don't worry if they are sticking up. When they get hot, they will lay falt and actualy melt into each other.
Caulk all the sideing edges and paint.
What is the door like? To protect it a little, you can nail a strip of the "L" flashing over it to get water comeing down the wall away from the door and the top edge of the wood. You can also put a piece of flashing on the top edge of the door to protect and keep it dry too.
Do the door the same as the walls, or replace it all together. I'd have to see better pictures of it to know anything more specific.
Have fun,
Eddie
