How can I legally get out of the apartment lease?

The landlord has to let you out.

The only way to legally get out of a lease that is still in effect is to amend the terms of the agreement, in writing, with all the other parties to the agreement. This would entail getting your landlord and your exgirlfriend to sign a document removing you from all of the duties, obligations and liabilities you contracted upon signing the agreement initially. Typically this is easy to get a former partner to agree to, but more difficult to get a landlord to agree to, especially if the remaining tenant wouldn't have otherwise qualified to lease the residence on his or her own, due to credit issues, etc. Additionally, accounting for the security deposit is often a tricky issue which need be dealt with. However, if the lease is month-to-month, you can terminate the agreement with proper notice, typically 30 days in advance.