How can you prevent yourself from infringing on other peoples' copyrights?

Always give credit where credit is due is the most important thing to remember - if you see something which eventually largely influences your work, make sure any original artists are credited for their influences, even if the work is not in the same category as yours (i.e. as an illustrator you take influence or ideas from a literary piece).

With access to photoshop and illustrator being widely available, the act of "tracing" is now becoming very common - this is where you take an image and use its outline with little to no modifications and redesign it as your own. This is extremely common with websites like deviantArt (which is not the best place to find inspiration by any means).

You cannot copy an artists style entirely and call it a reference - you need to be able to create your own works and if your work is near indistinguishable from another artists' work, you may find yourself in trouble.