Residence visas must be obtained before the issuance of work permits. Both applications are made through the Ministry of Labor, in Guatemala. Your employer will serve as your sponsor and will support you with your visa applications. They will submit all necessary documents to the Ministry of Labor.
In recent years, there has been a growing number of ESL teachers traveling to Guatemala on tourist visas to look for jobs. Once they find work, foreigners can stay in the country while having their visa status changed. However, prior to being issued with a work permit, you are not yet allowed to undertake paid work. Both residence visas and work permits are good for a year, and are renewable.
A general overview of what to expect teaching English in Guatemala