It varied. In 1833 Congress created the Dragoon or Cavalry regiment and fixed its size at 1,715 men plus 34 officers. The 1,715 included support personnel - teamsters, wagoners, blacksmiths, farriers, saddlers, musicians, quartermasters, cooks, doctors, hospital stewards, etc. A regiment was divided into 3 battalion of 4 companies or 6 squadrons of 2 companies, or some combination of that. In 1883, companies were renamed troops and squadrons of 4 troops replaced the battalions. In most cases a troop was 100 men plus noncoms and officers, it could be as little as 82 men with noncoms and support personnel bringing the number to 100.
Here is a reasonably good explanation:
http://ehistory.osu.edu/uscw/features/regimental/cavalry.cfmThis will give you an idea of the support personnel that could be attached to a regiment:
http://www.westernfrontassociation.com/great-war-on-land/43-britain-allies/241-cav-regi-big.html