Right now, you may be despairing that all your structures are going to be afflicted, and you'll never fix them. The second part of that statement is wrong (sorry, I can't say about the first), since indeterminacy can be cured without seriously reworking a structure. As opposed to the more technical definition given in the last paragraph, there is another, more common sense definition. Indeterminacy is caused when there are more supporting beams or forces than the structure needs to stay in equilibrium (upright, or however else you want it to stay).
A common example is a simple square, strengthened by two cross-pieces that don't touch or connect (notice the lack of a pin holding them together in the drawing at right). This structure is indeterminate, because only one cross-piece is needed to make the structure stable. The second piece is only redundant. The indeterminacy could also be shown by applying a force to it and working it out yourself or inputting it into our web programs. If you run up against indeterminacy either on your own or when using our programs, make a check for redundant beams.
Another case contributing to indeterminacy are joints with only two beams that aren't lined up (so they aren't forming a perfectly straight line) leading into them. It's ok to have these, (really!) but only as long as you have an external force acting on them (like the load or one of the supports). Otherwise, both of those two beams will end up having to have a force in them with magnitude zero. Why? Because there's no way that one of the beams could resist a force exerted by the other one. It would just move along with it, so it wouldn't be in equilibrium. Think of sticking your two index fingers tip-to-tip. Exert a force on one finger and the other one moves (you're not allowed to tighten up your knuckle, all joints have to rotate freely, remember?). The only way to keep your fingers from moving would be to have someone put their finger (an external force) pushing down from on top. You yourself can recognize this condition in a structure and correct for it, either by removing the beams altogether or pre-setting the magnitudes of the forces in them to zero.
At the other end of the spectrum is a condition where there are too few beams. Now, the structure won't be stable at all. This condition can come about when you don't build with triangles, and instead have squares (or worse!). Remember, all joints can move freely, so there's nothing holding a square from collapsing. If you're figuring out the forces in a structure by hand, you'll find that you come to a joint where there is a force acting in one direction, and no way to counteract it.