It depends on the terms of the lease, but it's hard to imagine a lease that would allow to do this unilaterally with no strings attached. That means it actually depends not on how much you like your landlady, but on how much she likes you.
In general, by signing the lease you assume a contractual obligation to pay the rent every month for the entire term of the lease. In theory, you can be sued if you don't do that.
In practice, a lot depends on your relationship with your landlord, as well as the rental market in your area. If the landlord can easily find a replacement tenant, they may be willing to allow you to leave early. If the rental market is slow, they will be more likely to hold you to the agreement. Obviously, if you have a good relationship with the landlord, they may be more inclined to go easy on you.
As far as telling your landlady you want to terminate the lease early, unless she's a particularly nasty person, you can just go ahead and tell her you'd like to leave early. What you can't do is actually stop paying rent. If you're on reasonably good terms with your landlady, you could just tell her your situation and say you'd like to move out. She may be willing to work out an arrangement where she lists the apartment while you're still living there, allows prospective tenants to view it while it's occupied, and then has you move out if and when someone else wants to move in (e.g., at the end of the month). Again, exactly how this works will probably depend on the rental market.
Assuming you're in the USA, here is a useful page with some info on breaking a lease. As mentioned there, the legal details vary by state.