If the lease does not provide for the landlord to repair the unit, the tenant must make and pay for repairs. There is not much that a tenant can do to hold the landlord responsible for minor repairs. The tenant may have some very limited recourses in cases where a landlord's failure to make repairs resulted in serious long-standing habitability problems such as rodent infestation, no working plumbing, or generally abysmal conditions.
In every lease agreement (unless expressly agreed otherwise) there is an implied covenant of enjoyment. This means that the tenant has a right to have possession of the unit without interference or disturbance by the landlord. For serious problems that make the unit unlivable, a tenant may be able to invoke this covenant, refuse to pay rent, and move out. However, the tenant is not allowed to refuse to pay rent because of the problems and then continue to live in unit. A tenant may contact the local or state health department or the local housing department to report.
Hazards in the unit that pose a threat to health or safety. Although enforcement varies from locality to locality, a report to the appropriate department can prove helpful. The landlord may be fined for failing to correct a code violation. Be aware that some departments will declare a unit unfit for occupancy if the landlord fails to correct the code violation, leaving the tenant with no choice but to move.