Photos are taken by a camera. They are a visual recording of light at a given time.
Graphics are different, they are created from scratch- they are not necessarily a record of reality. They are generally created by designers using computers.
Some tools used by professionals are:
software:
For graphics, there are industry standards such as Adobe Illustrator, Corel Draw, Xara.
These are quite expensive and have a bit of a learning curve. They are powerful tools and allow a skilled and creative designer to create amazing images.
You can download trial versions of the Adobe range which will work for 30 days for free.
there are free image editing programs out there too, such as artweaver
A graphics tablet - this is like a virtual pen, whatever you "draw" on to the surface of the tablet is reflected on the computer screen - ie into Adobe Illustrator. Different modes allow you to shade, draw, color, etc.. with your pen.
many people make do with just a mouse to draw their images.
another option is to draw by hand on paper, and scan the images into your computer. Scanners are quite cheap these days.
I suggest you download the Adobe Illustrator trial, and follow a tutorial. You can just use your mouse for drawing. It will take a bit of dedication and time, but if it's something you really want to do, you will just have to stick at it.
Don't try to jump straight into the program, you will just be confused and frustrated. Find a good tutorial and follow it, even if it seems a bit dull at first.