Honestly, your questions might not be as easy as you think, not that anything is especially hard it's just that there may be multiple answers to your question.
For some people like me, it's simply a matter of putting pen to paper and drawing out all the terrain features - then digitally scanning it into my PC, then using my favorite software to apply colors, bevels, drop shadows, etc to make a final map.
Some people use image editing software like Adobe Photoshop or GIMP, some use vector drawing software like Illustrator, Inkscape, Corel Draw, Serif Drawplus, or Xara Designer (the last one, I use), and some people use dedicated mapping applications like Campaign Cartographer, Dundjinni or Fractal Mapper - it really depends on which paradigm best fits you, and which software you are most comfortable using.
Go to our software forum and you will find lists of most of the applications many here use for creating their maps. Sometimes it's best to view the Cartographer's Choice forum and look for maps you like, then follow the artist/cartographer to see which software applications they used to create it. Once you've settled on the right software - buy it or download it (some applications, like GIMP and Inkscape are FREE).
Then go to the tutorials forum and search for specific tutorials using whichever software you decide on - and start learning. Once you start to create any map, post your work in progess, in the WIP forum to get comments and suggestions by the mapping experts on this site.
Really as far as software and techniques go - one size does not fit all. There are as many different applications and techniques to mapping as their are cartographers. Some software has huge numbers of people using it like Photoshop and GIMP, some like my choice in Xara software, there's only a handful of people using it. Explore the site and go from there.
Good luck in your mapping education endeavors!