Do surgery residency (5 yrs).
2 years of research during residency (usually between PGY2 and PGY3 years) is typical/highly advantageous for surg onc applicants.
Do surg-onc fellowship (minimum 2 more years, or more, depending on depth and extent of research).
So on average, at least 9 years of post graduate training before finishing.
Also, Breast Oncology (breast surgery) fellowships are different than Surg Onc fellowships (which does include breast), but both are under the guise of the Society of Surgical Oncology (SSO) if you do an internet search for more information.