How fast do cancer cells divide (compared to normal cells)?
Tumors can be benign (they don't bother you at all eg: a mole which does not change) and malignant (also called cancer).

The difference is based on:-


Degree of differentiation - How much the tumor cells resemble the normal cells
Rate of growth - In general (over generalised) benign tumors are slow growing while malignant tumors are fast growing
Spread to nearby tissues - Benign growth don't cross tissue planes as defined by basement membranes/fascias, while malignant tumors invade across tissue planes
Metastasis - Spread to a remote location in the body through blood, lymph vessels, transcoelomic (peritoneal, pleural, pericardial spaces) routes - This is ONLY seen in malignant tumors.


Coming specifically to rate of growth, these factors must be considered:


What is stated above in 2 is the general case:

Malignant tumors a.k.a cancers grow fast
Benign tumors are slow growing
That being said some benign tumors grow faster that malignant tumors. Eg: Fibroid - grows very rapid under the influence of estrogen as in pregnancy

The rate of growth of malignant cancers depend on their degree of differentiation (look point 1 above).

Well differentiated cancers grow slow - Cancers that are very similar to normal cells are considered to be well differentiated
Poorly differentiated cancers grow faster based on the "poorness" of differentiation,i.e. the worse the degree of differentiation, the faster the growth. Totally undifferentiated (unidentifiable as any tissue type) are called anaplastic cancers and these grow the fastest

The rate of growth of cancers may vary over time 

Due to excessive division probability of mutation is high and a sub-clone may emerge with faster rate of division thus a previously slow growing cancer could suddenly start growing fast 
Due to the same process some cancers may suddenly decrease in their growth rate and may eventually even vanish! (become necrotic and get cleared away)



This is taken from Robbin's Text book of Pathology,Ed.8, chapter 6

Edit 1: 
To know the numbers you need, you have to find out the rate of increase in volume (by measuring size at two points in time) and divide it by the approximate volume of one cell. This will give you the number of cells that has newly divided within the two measured points (growth in interval). Which can then be converted to cell divisions per second. 

As pointed out, the rate is going to vary extremely, based on the cancer type.