From experimental data, a critical tap will range from 350% normal tap damage to 9500% normal tap damage. This data will appear skewed to the right in the same red font as normal, only slightly larger, with the majority of critical hits between 400% and 500% tap damage. This data is based without any heroes who would buff the critical damage amount.
Critical hits do visually make the screen shake a little bit. At times, especially when running Shadow Clone, War Cry, and/or fast tapping, it may be hard to keep track of this shaking, but it denotes as you land the critcal hit.
Critical hit chance can be buffed by critical strike which is an active ability that can also come a fairy chest. Critical damage and critical chance can be improved from upgrading heroes to certain levels.
Your current critical tap chance and critical hit multiplier totals can be found in the Statistics icon in the Settings which is found in the upper left hand corner, denoted by the gear symbol.
Crit data collected (http://pastebin.com/Xk2WnDh6)