Disclaimer: This answer is from a general point of view, not specific to the United States.
This is essentially a contractual dispute: Your have entered into a contract with the landlord, which states that
- you pay the landlord a monthly rent, and in exchange
- the landlord lets you live in the appartment you rented, and maintains it in reasonable condition
You think that the landlord is not keeping up their side of the deal by neglecting maintenance.
In general, you must establish:
- that the landlord indeed owes you what you are expecting
- that they did not provide it to you in a timely manner after you requested it
To clear up the first point you must establish what exactly the landlord is required to provide - this can be either explicitly in the contract or implicit due to local law or general consensus. This highly depends on the nature of your contract, and on local law and customs.
To clear up the second point, you must establish that you explicitly told the landlord about the problems and asked for a solution, and that the landlord did not address the problems. Again, exact requirements, timeframes etc. vary a lot, but in general you should demand changes in writing, document them and explicitly specify reasonable time limits for the landlord.
- find out whether what you expect is covered by your contract or local law / customs
- ask your landlord in writing to fix it, and set a time limit
If that fails, you can probably sue, and/or unilaterally cancel your contract.
Again, details will vary with jurisdiction.