Grab a hook and a hammer and get to work. Seems easy enough, but there's definitely some science to hanging art properly. With these three key measurements as a starting point, you can't really go wrong.
57" - 60"
The Ideal Height for Art on a Wall
2" - 6"
The Ideal Distance Between Pieces of Art
6" - 8"
The Ideal Distance Between the Bottom Edge of Art and the Top Edge of Furniture
The first figure tells you that the center of your piece should be around 57 to 60 inches from the floor. If you're hanging a grouping with many pieces, try to find the visual center of the arrangement and work from there (map it all out on the floor ahead of time).
The second figure suggests that there should be 2 to 6 inches of room between frames in a gallery style or grouping. Any less, and the arrangement becomes too crowded. Too much space, and the frames lose their relationship to each other.
The last number is a guideline that keeps your artwork grounded around your furniture, such as the headboard or the back of the sofa. This figure might come into odds with the first, especially if you have very low profile furniture. In that case, I would suggest that you find a happy balance, bringing the center height of the art down to sit closer to the top of the furniture in the room.
The fine print? You can absolutely break these rules anytime you'd like. I've seen some really compelling gallery walls where the frames touch each other. And in rooms where the eye level is raised or lowered (because they're seated on very low furniture, or because they're children) the artwork can move up or down accordingly.