Do I have dual citizenship?

No--it means you only have U.S., because you were born in this country. If your parents did not register your birth, you will have to contact your local Embassy/Consulate and inquire.
Once that is done--you can obtain a passport and have dual citizenship.
Leave the US. and enter Honduras on your Honduran passport--
Enter the United States on your US passport.
I carry citizenship from two different countries--I leave the US and enter my homeland country on the homeland passport--I leave the homeland country on my US passport and enter the US on the US passport.

Have you gotten an American passport yet--if not, please do so.
You can have dual citizenship if your parents have registered your birth--you have received a certificate and also applied for and received a Honduran passport. Your parents can help you obtain one--consulate your local embassy/consulate/magistrate. If this has already been done--then all you need to do is apply for your passport.
Once you have both passports--please remember you leave the U.S and enter Honduras on that passport.
When you return--you return into the U.S. on your U,.S passport.

Most likely. See this: http://www.multiplecitizenship.com/wscl/ws_HONDURAS.html

No, you are a US citizen because you were born here. You may be eligible to apply for dual citizenship, you would need to look into the rules in Honduras and probably visit a Honduras embassy or consulate. They can help you.

Madman has the belief different than that Germany does enable twin citizenship below specific circumstances (below age 23, twin citizenship at delivery, etc.) Mexico on the different hand does no longer enable twin citizenship. maximum Mexican individuals that have a US and a Mexican passport are US voters and Mexican nationals (2 quite a few issues).

You have the potential to be a dual citizen of the US and Honduras but you would have to be registered as a Honduran citizen in order to be called such.

There are always two questions to be answered when it comes to dual citizenship:
1. Do both countries concerned permit it?
2. Are you a citizen of both countries under their own laws?

1. Honduras recognises dual citizenship (or to be more exact, it doesn't require you to choose between citizenships - this is the usual practical issue). The USA is not keen on it and some laws will even say that it is not recognised, but the actual position according to the State Department is that US citizenship can never be lost unless it is formally renounced. http://travel.state.gov/travel/cis_pa_tw/cis/cis_1753.html

So far, so good.

2. Anyone born on US soil is a US citizen. As far as I understand Honduran law, the same applies there, and any child of a Honduran citizen born abroad is a Honduran citizen. http://www.multiplecitizenship.com/wscl/ws_HONDURAS.html

Therefore you have dual citizenship. The one thing to bear in mind when travelling internationally is that the US requires that its own citizens enter and leave the US on a US passport, so even if you want to visit Honduras you will still need a US passport to leave the US. The practical problem is that if you have only a Honduran passport, the immigration officer will expect to see a US visa in your passport when you return and it will cause no end of trouble if you don't have one. A US passport is slightly cheaper than a US visa anyway and much easier to get with your US birth certificate.

Suprise surprise, the only dual citizenship allowed by US is, US and IsraHELL and no other as far as I know.