Your landlord has an obligation to keep your residence in good condition. This doesn't mean that cosmetic updates -- like updated trim or new bathroom fixtures -- have to be made, but that the residence has to be habitable and safe. Safety issues like broken banisters and exposed wiring need to be fixed.
That being said, your landlord can't typically just come into your residence to make the repairs without letting you know. You may not own the property, but you do have a right to privacy since you signed the lease. Your landlord should contact you, work out a good time to come make the repairs, and then stick to that schedule so that you know what to expect.
There is one exception to this rule, and that's when there's an emergency. If there's a fire or a flood, for instance, it may be prudent for the landlord to simply enter without contacting you to correct the problem. This allows landlords to reduce the amount of damage that is done and protect the property when quick action is needed to do so.
So, how much notice should you get? The general rule is that repairs need to be made as soon as they can, typically within 24 tp 48 hours. This timer starts when you tell the landlord about the issue, and many will schedule a repair time with you right then.
If your landlord neglects your property and repairs aren't made within a reasonable amount of time -- which may not always fall within the 24 to 48 hour guideline, depending on the circumstances -- you may be able to seek compensation for any resulting injuries. If you tell your landlord about a fire hazard, for instance, and nothing is done for a month, you might be able to seek compensation for injuries suffered in a house or apartment fire.
Source: FIndLaw, "Landlords' Duties Regarding Repairs, Maintenance, and to Provide Notice to Tenants for Entry," accessed Nov. 23, 2016