How can I determine the minimum shutter speed at which I can effectively avoid camera shake while hand-holding the camera?
The general rule is
1/EFL (equivalent 35mm focal length) without IS.
That means if you're on an APS-C, 1/(FL * 1.5~1.6).
The improvement IS gives is given in stops. One stop is applying a power of two, so, the final calculation is:
Everyone shakes different amounts, and even interacts differently with each IS systems.
The general rule of thumb for 35mm (full frame) has been the reciprocal of the focal length.
This means that for a 50mm lens, the minimum shutter speed when hand-holding is 1/50 sec.
1/(focal length) = 1/50
Since this is usually not an option, 1/60 sec is the next option.
Since the move to digital and multiple sensor sizes, the generally agreed upon rule is that the effective focal length is the number to keep in mind.
So, on a APS-C cropped sensor, a 50mm lens would need a
1/(50 * 1.6) = 1/80 sec.
On a longer telephoto, say a 300mm on a full-frame (35mm) you would need 1/300 sec.
Camera (and lens) makers are now adding image-stabilization to their lenses, which lowers the shutter speed needed. Generally the makers will rate the level of stabilization in stops. Keep in mind these ratings are used for marketing and may be a bit inflated, but I am going to do my calculations based on the numbers being correct to keep it simple.
If you are using a 100mm lens with a 2 stop image stabilization system on a APS-C cropped sensor then:
(1/(effective focal length)) * (2 ^ image-stabilization-stops) (1/(100*1.6)) * (2^2) (1/160)*4 = 1/40 sec
A couple of answers have already mentioned the 1/FL rule of thumb. Keep in mind, however, that this is only a rule of thumb, not an iron-clad law. Depending on how steady you are, you may find that you can (or must) adjust it.
Good technique is critical here. The same techniques used by target rifle shooters work nicely. First, get the steadiest stance you can: prone is best, kneeling second best, standing up your last choice. If you have to shoot standing, put your left hand directly under the lens and brace your elbow against your chest if possible (especially important with longer/heavier lenses). Take a fairly deep breath, then let it about halfway out before you squeeze the shutter release.
Okay, mine is not a technical answer, but I think it has some merit that the technical answers lack: empiricism. Try using different speeds and see what you can hand-hold.
For each lens (and zoom setting, if applicable), handhold the camera while on shutter priority,and see what the slowest shutter speed YOU can use is without shaking the camera. Different people have hands that shake to different degrees.
By the way, I would check out whether or not it is blurry on a monitor, not on the camera LCD. You just can't see clearly enough to be sure whether there is blur on the LCD (unless you have a much better quality LCD screen than I've seen.
You can determine the minimum shutter speed to avoid camera shake by
1) applying the following approximate rules of thumb. (See Wikipedia article - rule of thumb)
2) or carrying out careful measurements, as I did.
1) The rules of thumb
a) With NO image stabilisation
The approximate rules of thumb are:
Full frame cameras : min shutter speed = 1/focal_length
APS-C cameras : min shutter speed = 1/(focal_length*1.6)
Note that these are approximate rules and are heavily dependent on photographer technique, which is why they are called rules of thumb (my thumb and your thumb are not the same).
b) With image stabilisation.
Here the rule of thumb is to take the above calculation and increase the above shutter speeds by either two or three stops, depending on your confidence in the manufacturer.
2) Measured results
By conducting more than 1000 measurements under carefully controlled conditions I arrived at the following results. The fully documented study can be found on scribd.com:
A Study of the Effectiveness of Shake Reduction in the Pentax K7
The graph below shows the main result of this study. With a 50mm lens motion blur was kept below one pixel down to a shutter speed of 1/8 sec, which is more than acceptable.
This is effectively equivalent to the following rule (for the Pentax K7):
min shutter speed = 1/(focal_length*1.6) - 3 stops.
However at shutter speed below about 1/30 sec the result are critically dependent on photographer technique. The graph below shows how variability of the results increases rapidly at lower shutter speeds, which illustrates the importance of photographer technique.