You'll find your first set of dog tags fairly quickly in the game. When you are following O'Neal to get to the cargo bay you'll be working your way around a large yellow rotating machine (O'Neal calls it the Gravity Well). Fight your way around it and you'll come to a locked door Let O'Neal open it while you watch his back, Keep following and you'll go up a set of steps into a room and you'll see an Audio Log in front of you on a table. Fight the aliens in this room and enter a hallway. An Alien will come out of a grate in the floor in front of you. Kill it and it's buddy and then continue up a small flight of stairs, you'll see some shotgun shells and bag o ammo directly in front of you. Look to your right on a desk next to the doorway heading back out to the Gravity Well and you'll find your first set of Dogtags.
If you'll having trouble following this.. Sorry I did the best I could with directions seeing as most everything looks the same in the game.