Here is the graphical design tutorial. It will be useful to understand the basics.
graphics, tutorials, softwares, designing, free training, downloads

If you are looking for some examples the XSitePro crew do a free header tool called XHeader.
You can find it here:
Free Header Graphics Software | XHeader

Hi Em, what are you trying to design? Headers, web sites, logos? Most tutorials are going to be specialized tutorials on the specific type of graphic or project you will be working with.

Once you have that down, the absolute best free online graphics tool is Pixlr > Photo editor online / free image editing direct in your browser - Pixlr.com

Update: It looks like you've updated the thread title to indicate that you are looking for help designing header graphics. In that case, assuming you are using Photoshop, here's a good tutorial > http://paulstamatiou.com/how-to-make...header-graphic

If you want to use a free tool, here's a tutorial I created on creating a header graphic using the free online photoshop clone, Pixlr.com.

Yes, pixlr is a very good one similar as Photoshop.

anyway good free tutorials are here: Gimp Tutorials - Search for Gimp Tutorials on Pixel2Life