How much does a family history of colon cancer increase my risk of getting it?

Varies. The "family history" of colon cancer needs to be further clarified as to what type of family syndrome this is. A genetic counselor can help further define the risks and potential surveillance or treatment strategies. The increased risk may be small or may be very large. Specific genetic testing may be indicated.
Double the risk. If there is personal family history then the risk of getting colon cancer is usually double than that of the general population. If your family member was young when he/she developed colon cancer then you should have your screening colonoscopy done 5-10 years before the age that your family member developed cancer.
About 10% A family history of colon cancer, especially in a close relative, increases the risk of cancer 10% above the general population. If the relative was diagnosed at a younger age (40's) then the risk is slightly higher.

Related Questions

Is it recommended to get a colonoscopy at age 43 if there is a family history of colon cancer? What other tests are needed at this age?

Yes...get one done. The age depends on your family, history. Screening mammography, a complete family history may add genetic testing. A complete physical.
10 years before diag. A basic guideline is that in the case of a potentially inherited cancer trait, that we start screening 10 years before the presentation of a first degree relative, i.e. Parent or sibling. If the relative was diagnosed with colon cancer at age 53, we consider beginning screening tests at 43. Otherwise begin screenings as age appropriate, colonoscopy age 50, mammo age 40.