Slow down the work being done. This is the first reaction of most machinists, and helps gather information about where the chatter is coming from.
Look for points of rigidity, either on the tool or the workpiece. Look for any parts that are loose, or points of chatter that could be improved with stabilizing by tightening or bracing.
Experiment with speeding up the work. Chatter is a resonant phenomenon, which means it's highly dependent on hitting a certain frequency. If slowing down doesn't provide useful information, see if speeding up slightly helps move the work into a frequency that minimizes the chatter.
Change variables on the tool, one at a time. These variables depend on what tools being used. In the case of a cutter, changing the number of flutes being used may help. When using tool or drill bits, adjust the distance that the bit is sticking out. This can have a remarkable impact on chatter frequency.
Map the chatter behavior by noting when chatter occurs. Using a measuring tape and a notebook, note the measurements or positions related to the machine, toolholder, cutter and stickout. This can help develop a "map" of when the chatter occurs and what adjustments may help.
Consult the owner's manual for tools or equipment involved and more clues on adjustments that may help.