If anyone can give me some guidance here, it'd be much appreciated. I know the NaNH2 would dissociate and the NH2- base would deprotonate the terminal acetylene. I'm assuming the resultant product would act as some sort of nucleophile which would open the ring of the epoxide. The Na+ would form an ionic bond with the negatively polar oxygen after which the acid would protonate said oxygen, but I'm not entirely sure.
Basically, you are on the right track and answered the question. First, NaNH$_2$ is used as a base to deprotonate the terminal alkyne (see this Reagent Friday). Second, the generated nucleophile opens the epoxide in an S$_\mathrm{N}$2 fashion, usually adding to the lesser substituted carbon which in your case yields a quaternary alcohol after acidic workup (see also Opening of Epoxides With Acid).
(Note: Indeed you are missing the CH$_\mathrm{2}$-group where the nucleophile attacks in the final structure)
