The vast majority of artifacts are fairly easy to find. As you collect them you will see a message pop up on the right side of the screen to let you know how many of this particular artifact type you have obtained. For most people, the issue with these comes from obtaining the final few in a collection. This guide will help you find all 45 artifacts in God of War and unlock the Curator Trophy.
Artifacts are generally found next to slumped bodies of dead soldiers. The item will be right next to them. There are course plenty of instances where its just hacksilver, but this is usually a place to find them. Artifacts are hidden a little better than hacksilver drops, you will need to be going out of your way in most cases if you want to find them all.
The important thing to remember about the artifacts is that you DO NOT need to hold onto them. The items are there to be sold and if you go to a vendor you will see the message that says these serve no purpose other than to be sold. If you are low on hacksilver feel free to sell off all of these as there is no reason to keep them.