For the United States, the forces consisted of the Regular Army, U.S. Volunteers, and the state and territorial militias. The regulars did most of the actual fighting in this war (46 regiments of infantry, 4 rifle regiments, 2 light dragoon regiments, and 4 artillery regiments). The volunteers were temporary regiments, mostly infantry, but lumped in that category were up to 10 independent companies of sea fencibles, recruited among sailors for harbor defense (because of their expertise in handling boats), and about 17 companies of U.S. Rangers, recruited from experienced frontiersmen primarily to scout and combat hostile Indians.
There was no legal mechanism for drafting men directly into the U.S. Army. The President could call on governors of the states and territories to provide quotas of militiamen for federal service, but there was no way to enforce compliance, and some governors did not. With a few exceptions, able-bodied male civilians aged 16 to 60 were subject to compulsory militia duty when called by the respective governors, usually by lot, although some volunteered for active service. Around 400,000 militia were called out at one time or another during the war, but mostly for short periods from a few days to 3 months. Most of the militia service consisted of manning forts, patrolling, and escorting supply convoys. However, several thousand militiamen did serve in combat against British raids and invasions of U.S. territory, notably in the unsuccessful defense of Washington, D.C., and the repulse of British forces at Baltimore and New Orleans, and also in frontier districts against hostile Indians. Some also participated in offensives into Canada, especially along the Niagara River.
The National Archives would hold surviving original records of enlistments in the Regular Army and the U.S. Volunteer units. Other records exist of applications for land bounties offered as an inducement to enlistment in these units. Militia records would be located in the archives of the individual states. However, as veterans of this war aged, Congress created pensions for those who could prove their service for a minimum period (and their widows). This act included militiamen, as well as regulars and volunteers. Many records pertaining to bounties and pensions were published in the American State Papers, and can now be found on the Internet. Brief records of the service of officers of the Regular Army can also be found in Francis B. Heitman's "Historical Register and Dictionary of the United States Army" (U.S. Govt. Printing Office, 1903), which is fully available online at Google Books. Google Books is also a good place to find details about the activities of the various state and territorial militias, if you get creative with your search terms.