Solution: First step is to re-"unite" the pieces. They fit nicely into a grid, shown here.

Treating the dots as spaces, and the symbols as letters, it reads "MOVE THIRD AND FOURTH LETTERS AROUND". Third and fourth letters of what? Well, looking back at the symbols and the letters they were replaced with, we have four sets of two letters. For example, the two "Triangle" letters are M and A, which can form MA, the abbreviation for the state Massachussetts. The other three symbols give VT (Vermont), LA (Louisiana), and OH (Ohio). If we take the third and fourth letters of these states, we get: SS RM UI IO. Moving those around spells out MISSOURI, a US State and the solution to this puzzle.