Adam,
The main pieces of software used to make signatures or other types of image are either Adobe's Photoshop of Jascs Paint Shop Pro series. Both are relatively expensive but usually have 30 day downloadable trials available.
With regards to how to actually make the aforementioned graphics, well in all honesty there is no simple "this is how you do it". It's predominately a case of trial and error, playing around with the software and creating your own style and preferred methods.
That said there is a wealth of information available on the internet to help you achieve certain effects, and you can find tutorials on just about everything. A simple example of this is the post on these very forums that detail how to make a straightforward signature. These are great, but they only give you a small piece of the puzzle.
By working through these many tutorials you can start to build a core base of skills and techniques that will further the quality and type of work you can produce.
A simple search for "photoshop tutorials" on google will return a massive amount of possibilities (assuming this is the preferred piece of software to use). But for starters try checking out some of the following:
Photoshop trial:
Adobe - Photoshop CS3 editions Jasc software trials:
Home - Free Trials - Corel Corporation Photoshop Tutorial sites:
Photoshop Tutorials -- Absolute Cross Adobe Photoshop Tutorials - Tutorialized Good-Tutorials / Photoshop Tutorials + Flash Tutorials Spoono - Taste the Rainbow Hope this helps as a starter.
Graphic Making 
Linear Mode
