The first relic I found was on the first campaign mission, Harbin's Dig Site, past a locked grate door, around some turns and behind a puzzle door. After using your amulet to reveal the puzzle door, you have to shoot the buttons in the correct order (6 shots). The order is shown above the door. If you mess up 3 times, the puzzle locks you out for good and you'll have to reload last checkpoint to reset it. After the door opens, you go through some undead enemies and open a golden container to get the Calendar of Ra relic.
If you miss that relic, the next one is the Sickle of Thoth. It is on the ground inside the new area after you unlock the gate with the Scarab key.
Then a 3rd relic behind another puzzle door in a cave.
to view relics in your diary.
Not the best video I could have made, but here's the Calendar of Ra:
Sorry, this Game Clip has been removed