Everyone is going to violate copyright law to some degree, you don't have to be perfect. But you should be aware of what the actual copyright laws are, and try to uphold them to the best of your ability.
Never attempt to say that someone else's work is yours.  If you can't make your own work, that does NOT give you the right to take credit for someone else's.
Just becuase you give someone credit for something does NOT mean you have the right to use it. You ONLY have the right to use something when the creator gives you permission to do so. And only then and by his or her rules.
Be creative. Try not to borrow too heavily from other work.  We all "borrow", but I think you know when your work is a blatant "take-off" of someone else's. It's called plagarism. Having someone's work inspire a work of your own is perfectly acceptable, that's how we often learn.  But try not to make it too excessive. Put yourself into your work.
Never take OR modify someone else's work (be it drawings, text, html or web designs). Modifying something does NOT make it your own.  You are violating copyrights and vandalizing someone's work.
Due to some confusion:
The only exception to this would be modifications or use for parody, education or to illustrate a point. However use must be limited. This is covered under "fair use".  If you are unsure on exactly what entails "fair use". 
Please see Myth #4 "Fair Use" on the 10 Big Myths of Copyright.
Need an example of improper "modification"?*
 

This image is an original image of Disney's Demona.

Oh look.  I changed her outfit, her jewelry and all her colors.  She's a different character now.  So this image belongs to me right? Wrong.  This is a illegally modified image and a copyright violation.

Oh look... Demona's naked. I don't think I need to tell you that this is also a copyright violation.
If you see someone violating copyright law.  Inform the original creator of the violation so that they can deal with the violator properly.
*The three above images of "Demona" are from Disney's Gargoyles, an animated series.  They are used without permission of the Walt Disney Company or Buena Vista Television.  If you are curious, they are under fair use since they are being used to not only educate (about copyright law no less), but also used to illustrate a point in an article.