How can my boyfriend who I met online petition for me to go to the US?

Generally, there are requirements that a couple meet in person before triggering eligibility for a U.S. citizen to be able to succeed with a fiance visa (that would allow the foreign national to enter the U.S., to become married within the requisite time, and then file for adjustment of status to become a Permanent Resident). There are some exceptions, however, for that general requirement. There really is no substitute for you and your fiance to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.