lucille, I think you've partially answered your own question when you mention looking through the gallery and the houzz site. That is how you educate your eye and after a while you'll be able to analyze what it is you like and why you like it. In this case imitation is the the way to go. The most important rule I've learned is that pictures should not be hung in a vacuum. They have to relate to either other pictures or pieces of furniture. And, don't hang pictures too high unless there are other pictures below them or even a structure, such as a doorway. I hope this has helped a little bit.

Here are a few things I've learned, mostly the hard way, LOL... and mind you, these are just my opinion.

Pictures in groups benefit from some sort of unity. This can come from color -- the color of the frames, the color of the mats, a color in the artwork itself. This can also come from the style or the texture of the framing.

Or maybe the art is all by the same artist, or they have a common subject -- from architecture to botanical prints. They may come from a certain period or use the same medium, nature photography, for example.

Pictures hung in groups look best if the distance between the frame edges is equal. BUT don't hang them too far apart. The distance between them should be no more than 1/3 the width of the artwork itself. Don't be afraid to hang pictures close together.

You can experiment with your arrangement without putting holes in your wall if you cut out brown paper shapes traced from your artwork, and then tape those shapes to the wall. You can then move these around till you find an arrangment you like, BEFORE you put holes in the wall.

[You can also use these squares to find the exact placement of the nail. After you cut out a square, hold it on the back of the frame, aligning the corners. With your finger, feel for the place where it will hang -- the apex of the wire, or the serrated hanger attached to the back of the frame. Using a pencil, poke a small hole in the brown paper where the nail would go. Then, when you tape the brown paper cutout to the wall, and when you find the right spot to hang your art, you can simply make a pencil mark on the wall, right through the hole. Voila! That's where your nail will go.]

In a large grouping of frames, make an outline on the wall with masking tape of the entire group. That is, make a big square or a big rectangle and arrange your paper shapes within it, so that the edges of the artwork comprise the edges of the tape outline.

If you're making a horizontal line of different-size pictures, align the bottoms of the frames in a line. You can do this by putting a piece of masking tape on the wall. Make sure the distance between each frame is the same.

The center focal point of the artwork should be eye-level.

Artwork with a lot of small detail should be hung where people can get close enough to look at it. Larger, more abstract pieces should be hung in larger rooms, so people can appreciate it from a distance.

What is your decorating style? Traditional style is more formal and symmetrical, while modern can be more asymmetrical. Cottage style is more eclectic and artwork can be arranged in a more casual pattern.

Hope these random tips helped.

mcclarke - excellent tips about arrangement, groupings and having every straight!! I'm taking notes as I go!

Looking at all the pictures of groupings in this thread helped me work on my walls.

Here is a link that might be useful: thread on Salon Style

I like to break up artwork (meaning framed pictures) with other things. My "picture wall" has three types of wall clocks---one a fancy walnut antique (which is the "centerpiece"). a 1930 children's painted metal clock, & the other a rather small modern clock, along with a couple of antique thermometers--one oak, the other copper interspersed. The artwork itself has absolutely no relation to each other, whether by color, size, frame or subject. It all works very well for a more eclectic grouping.

Thank you all for your ideas. Boop, thank you for that thread you linked. Not only did it give me ideas, the many beautiful groupings of pictures made me realize something about myself: I had come to this forum and I was going to totally change out what I had for a spare, airy look.
In preparation for painting, I took down my pictures and my many hanging copper pots. I miss them. Perhaps what I am after is not a whole new look, but rather a more studied way to have and display the things I have collected and cherish.

There is a lot of inspiration here, but more, I love that everyone puts their ideas out on the table like chocolates in a candy dish, allowing all who pass by to take one or several rather than force feeding set ideas.
Y'all are so awesome.