Cancerous cells are cells that, through cumulative DNA damage, are unable to undergo apoptosis (programmed cell death), so really the question boils down to how fast can these cancerous cells replicate. That depends on what cell it is and where it's located. Location and cell type are crucial because they determine how quickly the tumor can reproduce and/or breach organ barriers and metastasize (spread to other areas of the body).
The speed of growth can be generalized by looking and the 'histology' and 'differentiation' of a cancer.
The differentiation of a tumor refers to how the cells look under the microscope. Cells that look normal are termed well differentiated. On the other hand, if the cells appear very abnormal they are termed poorly differentiated. Poorly differentiated cancers tend to grow quicker than well-differentiated tumors.
The histology of a tumor relates to the pattern the cells form as whole when viewed under the microscope. This influences a tumor's rate of growth and spread. For example in lung cancer, small-cell cancers tend to grow and spread very rapidly. In contrast, non-small cell lung cancer tends to grow and spread at a slower rate.
There's more complexity to this, but the only real way to determine the rate of growth is to observe the patient and their cancer development over a period of time - it can vary wildly.
Additional information and resources:
Tumor grade (differentiation and growth speed indications): http://www.cancer.gov/about-cancer/diagnosis-staging/prognosis/tumor-grade-fact-sheet
Types of cancer (what different types of cancer are produced by different cells/locations): http://www.cancerresearchuk.org/about-cancer/what-is-cancer/how-cancer-starts/types-of-cancer
Example of histological indication (click the answers button): http://www.pathguy.com/histo/007.htm