OK Brent, this one's for you.
Over in this thread, I describe the types of hardware we typically use to install artwork at my job as a Picture Hanger to the Rich and Unfamous. This tutorial discusses how I hung a painting in my house using straps and hooks. This isn't the only way to hang a picture, but it's how I did this one.
For starters, here's the test subject. This is the only painting in our house that wasn't done by my mother-in-law. I honestly don't know why it's in our house, but it is.
For starters, the piece is too high. It needs to be lowered a few inches. Also, it is hanging from a cable that's attached to a single hook on the wall. Not very secure, and it doesn't like to stay level.
First step: Remove the cable. It was held on with thumbtacks. I'm amazed it's held the picture for (I'm guessing) the past 30 or 40 years:
I replaced the cable with a pair of 3-hole straps. This picture is lightweight, so the 3-holers are overkill, but that's what I had on hand. It's important for the straps to be in the same relative position on both sides of the frame. In this case, I measured down 8" from a square point on the back of the frame, then used that mark to locate the top screw on each strap:
The 8" distance is an arbitrary number. I simply try to get the strap somewhere around 1/3 of the way down the frame. It's only important for both sides to be the same.
After the straps are installed, I need to know how far below the top edge of the frame the hanging loop is. Since this frame has a beveled edge that's about impossible to accurately hook a tape to, I turned the frame upside down and measured from the floor to the loop. In this case, it was 9 3/4". I also measured how far apart the straps are. On this frame, they ended up 33 3/8" apart.
Now, the math part. If I can do it, anyone can.
First, I know I want this picture centered on the wall. The tape tells me the wall is 51 3/8" wide, so the center point is 25 11/16" from the edges of the wall. I put a pencil mark at that spot, in an area I know will be covered by the artwork. (Since I need to find the center of things every day at work, I carry a center-finding tape from Lee Valley on my tool belt. I didn't have it with me when I hung this piece, so I had to figure it out the old-fashioned way.)
Next, I need to decide how high to hang the picture. Quite often, we hang artwork in homes at what we call "60 center", meaning 60 inches from the floor to the center of the picture. That's a height that's a comfortable viewing level for most people. We'll adjust that height up or down to accommodate furniture or the client's preferences, but 60 center is almost always a good starting point. That's where I decided to hang this piece.
Instead of describing the math, here's a picture that shows how I determined the top of the picture needs to be 74 3/4" off the floor:
Once I know where the top will be, I can figure out where the hooks go, since they need to be 9 3/4" below the top of the picture. That ends up being a nice, even 65 inches from the floor. (74 3/4" minus 9 3/4" equals 65".) I make a pencil mark on the wall 65 inches off the floor, then use a level to intersect the centerline (upper mark) of the wall with the 65 inch height (lower mark):
That lower mark is the centerline of my hooks. The straps are 33 3/8" apart, so half that distance will be the distance from the centerline to the hooks. That's 16 11/16". Handy trick for measuring from a point and marking the wall: Use the tape hook itself to make the mark. Hold the distance marker on the center point (left hand in this pic, holding the 16 11/16" mark on the certer), then rub the tape hook in a small arc on the wall:
After marking both sides, use a level (using the center mark as a reference) to mark the height on each of the arcs:
Hold the bottom of the hook to that line, and nail it to the wall:
Do it twice, and you've got two hooks:
At this point, I hung the picture, and determined that it was slightly out of level. This can be caused by drift when driving the pin nails into the wall, or when driving the screws into the frame to attach the straps. With this type of hooks, adjustments are easy. In this case, the right side was a bit higher than the left, so I wanted to drop the right side about 1/16". (On drywall walls, you should always lower a side, not raise a side. If you raise the hook, the drywall below the nails has holes in it, so it's not a good anchor. If you lower the hook, you've got solid drywall under the nails.)
What lowering a hook may look like:
That little bit of adjustment was enough to get the results I was looking for:
And the final result, in the new, lower position: