Let's see...
The sample which was used in the experiment came from Xen. When Gordon pushed it into the beam, it caused a "resonance cascade" which caused a portal to open between Xen and Earth, causing all the nasty critters to be teleported into Black Mesa.
The military which were sent into Black Mesa had orders to kill everyone associated with the project, most importantly Gordon.
Gordon managed to survive the horrors and many dangers that lurked inside Black Mesa, but meanwhile, unbeknownst to him, he was being watched by the G-Man.
Eventually, Gordon reached the Lambda Complex, where he was teleported to Xen to take out the alien leader, Nihilanth. Gordon was succesful, and the G-Man saw an opportunity to make himself known to him.
The G-Man says to Gordon that "The borderworld, Xen, is in our control, for the time being." Who he refers to with "our" is uncertain. He then continues "I have recommended your services to my, eh, employers. They agree you have limitless potential." Most likely the "our" from aforementioned quote refers to the G-Man and his "employers" whoever they are.
The G-Man then offers Gordon a job under his supervision. However, since Gordon knows more about the resonance cascade incident, Black Mesa, and Xen than any person should, the G-Man threatens to kill Gordon if he doesn't accept. Naturally, Gordon accepts the G-Man's offer and is put into stasis for an indeterminate amount of time to be put back into action whenever the G-Man sees fit.