If you had a plane with a flutter problem, how would you investigate it?
If you only had a problem at the high end of the airspeed envelope, the simplest fix would be to draw the red line on your airspeed indicator (if you have one) a safe amount below the problem area. Anything else is going to require the application of some Do-Re-Me $$$.
If you have a flutter problem that blocks you from the heart of your operating envelope, you either have a museum piece or you will have to figure out and fix the problem.

Modern electronics has brought the price of things like accelerometers down into the accessible range. You would wire up a bunch of light weight accelerometers to a computer to collect data. You would decouple the aircraft from the ground by loosening the bungee cords until the aircraft was resting only on the cords and not on either the up stops or the down stops. Also put some soft rubber under the tail skid. The final piece of equipment would be an electric motor driven eccentric weight that would need to be firmly attached to aircraft structure at various locations during the test. You would have to be able to control the speed of the electric motor accurately.
What you are looking for would be the resonance frequencies and modes of your particular aircraft. You would probably start by looking at your control surfaces and determining how they respond to vibration. You would then move on to major structural elements. You could also use a visible medium such as a light coating of dust to observe the nodes (relatively stationary areas) of the vibration modes. The first five modes in ascending frequency order are probably sufficient. You need to move the exciting eccentric weight system around just to be sure you didn't accidentally couple up to a nodal point.

When you finish this exercise, you would have a fair idea of your aircraft's vibration modes and frequencies. You probably would not be able to discover unusual coupling situations (like the 747 model wagging its tail and twisting the wings). Probably the best way to record this data would be on a series of maps of the structure with the nodes and anti-nodes drawn in.
Before you proceed further, you might want to investigate adding mass balance to control surfaces to reduce their response to vibration. You would then retest the new configuration.
The next step is to calculate what exciting frequencies are likely based on Reynolds numbers your plane would be operating at and the dimensions of the surfaces. You would compare these exciting frequencies to the resonance frequencies that you had just measured on the actual aircraft.
Ideally the exciting frequencies and all the resonant frequencies will be significantly different, but if not, you have identified a potential problem requiring correction or at least careful evaluation.
Finally, you would move to test flying using exciting devices such as the one described here:
http://ntrs.nasa.gov/archive/nasa/ca...2002119573.pdf
Here is where the real dollars come in. Potentially, this type of equipment can damp oscillation as well as excite it, so it could add an additional layer of safety in the test flying program.
Warning, use the above information with care. I don't do this for a living, and I may have understated or mis-stated important information. To the best of my knowledge, this is what people who cannot afford flutter tunnel testing do.

Sid