what to do after a person has been deported?

It would be better for your boyfriend to obtain an attorney in the States as you will require a lawyer well-versed in US immigration law and not of Honduras. Any waiver application would not be filed in Honduras, but at a lockbox of U.S.C.I.S. in the States. I note that a waiver is not available if your boyfriend's only US relative is a three-year-old child. To obtain a waiver of the illegal presence bar for having been illegal in the country, you must prove that a US citizen or permanent resident parent or spouse would suffer extreme hardship if the waiver was not granted.Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

It doesn't matter where the attorney is as long as they are competent in filing for a waiver.  However, your boyfriend may not be eligible for a waiver depending on why he was deported.