How do I transfer to an international flight at Calgary Airport?

I'm flying to Monterey, California just before Christmas. I'm flying from a regional airport in Alberta to Calgary International before transferring to an American company and then flying to either San Francisco or LAX before transferring one last time to go to Monterey.
From my understanding, after you get off the flight from my starting city, I have to to collect my checked baggage from a special carousel and then go through security again? Because I'm going form domestic to international... I'm super confused!
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