Everyone joining the Army is required to enlist for a minimum of 8 years. Most spend a portion of that time on active duty (2-4 years) and the rest in a Reserve component. It is possible to sign up for all eight years to be served in the Reserves, but talk to your recruiter before you sign!
For a soldier entering directly into the Reserve, the initial time commitment is the same as any active duty soldier. Approximately 5 months (depending on the MOS) are spent on Basic Combat Training (BCT) and Advanced Individual Training (AIT). After that the soldiers that are entering directly into the Reserves are assigned to a Reserve unit, and the time commitments are much lower (unless the unit is mobilized).
For soldiers in the Selected Reserve, one weekend a month is set aside for Battle Assembly, where soldiers report to their unit in uniform for a weekend of training. The training could consist of MOS-specific skills, weapons qualification, taking an Army Physical Fitness Test (APFT), maintain their personal or unit's equipment (gas masks, trucks, etc.), receive health and dental screenings, or undergo a Soldier Readiness Program (SRP) to prepare for a deployment.
Two continuous weeks a year are also set aside for Selected Reserve Annual Training. For these exercises, soldiers may leave their home unit and travel to a large training area, work with other Reserve or National Guard units in the Army and with other branches of service.
Soldiers in the Individual Ready Reserve are not required to attend either Battle Assembly or Annual Training. They still may be called into service at any time as directed by the President or Congress, however.