Dog Tags are not difficult to obtain, but for those that are not aware of the process it may get a bit tricky.
First and foremost, get use to pressing the R1 button to initiate the first person view. That will be the key to obtaining dog tags.
Your objective it to sneak up behind the enemy and hold them up. To do that you need to be relatively close, initiate FPV and hold down the square button. Snake/Raiden will say "Freeze" and the guards arms will go into the air.
Next, get in the habit of shooting their radios (the item at the right on their belt). You can get this trophy for shooting ten of them:
You can destroy them with either the M9 (tranq pistol) or the USB/SOCOM (depending on what campaign you are playing). The reason behind taking out the radio is if, by some reason you botch the hold up, the enemy can't call for help giving you the opportunity to knock them out without fear of backup swarming your location.
Now, in order to acquire the dog tag, you need to get in front of the enemy, and aim at the guys head or crotch. Most enemies will shake about with a barrel aimed between their eyes, and the dog tag will appear. However, there are some "tough guys" who just ask "Are you going to shoot me?" instead of shaking. This is where you need the USB/SOCOM.
When you come across the "tough guys", shoot them in the right arm. They will get really squeamish after that. Also, if you shot their radio AND their right arm, they can't call for help and they can't draw their weapon.
Nearly every enemy has a dog tag. There are also dog tags on Olga during the tanker mission, and Fatman and Plisskin during the Plant mission. If you are unsure whether an enemy has a dog tag, look at their chest when they are being held up: if you see a little flash, that means they have one you didn't obtain.
Now, on the easier difficulties you will find multiple enemies in an area, and so you will most likely tranq a few to weed out resistance. This is fine, but I know it takes F O R E V E R for the damn soliders to wake up, especially on Very Easy and Easy. But there is a solution: the coolant spray. Continually spray this on a tranqed enemy, and they will wake up in a lot less time.
Questions, corrections and neg vote justifications below.