As a US citizen you can not be denied entry to the US once you are on US soil, with or without a passport. Other than a passport there is no set list of documents required, however you will need to be able to convince the immigration officials that you are a US citizen and/or prove your identity so documents such as a Birth Certificate, Green Card, Drivers License, etc will all be helpful. If you follow this path you WILL be taken to secondary screening, and you can expect the process to take at least 1-2 hours longer than normal.
However your initial problem is going to be making it to US soil. Without a US passport the airline will not let you board your flight to the US unless you have suitable entry documents, which means that you'll need either a Visa or an ESTA (if your other passport is from a country that is a part of the US Visa Waiver Program).
If entering under the VWP, or most types of Visas, then you will also need to hold an onward/return air ticket as proof that you will be leaving the US at the end of your trip. Obviously once you arrive and enter the US as a citizen this will not be required, but without it it's highly likely that the airline will refuse boarding without it.
Also be aware that as a US citizen you MUST enter the US as a citizen. ie, even if you have obtained a ESTA and a return ticket, you can not legally use your foreign passport to pass through US immigration. These will be required to allow the airline to carry you to the US, but must NOT be actually used to enter the country.
In general, your best option is going to be to contact the local US Consulate and obtain a US Passport. This will save you a lot of trouble not only before your trip, but also when you actually arrive in the US.
If you intend to leave the US again in the future you will also need a US passport for that - it is illegal for a US citizen to leave the US using a non-US passport.