The cartographer requires a few materials to maximize his/her working potential. Paper, obviously, is a must. Sometimes doodling a map on the wall of your Vertebrate Zoology class is fine, but to really create a good map, you need paper. For the rough draft I recommend lined, loose paper. This will suit you fine until you have the map totally laid out. For the middle drafts, I recommend regular, loose leaf, printing paper. This will give you a clear view of your rivers, shorelines, etc. And for the final, all important draft I recommend the semi-sturdy, thick paper that has the flexibility of construction paper and that does not allow ink to seep through it. 

Pencils and pens are the prime drawing tools of a map maker, but I find hi-lighters, colored pencils, and even crayons useful for indicating separate things on the rough and middle drafts. A regular, 2 hardness pencil is fine for making your first draft, and erases very well. A good pen is a definite must. Any final draft that you do must be in a good, well defined black ink. Regular BIC^TM pens leave a greasy ink, and I prefer micro-point ball-point pens for my maps. 

People make mistakes. Cartographers definitely are people. In this light, you will need a very good eraser. I prefer the large gum erasers that rub off very easily and leave almost nothing stuck to the paper. Likewise, they leave the paper in place. Other erasers have a tendency to leave pink streaks on the paper, or they tear a swath of paper away where they erase. I like my paper intact, so I refrain from using the eraser on the end of my pencil on my middle and final drafts. 

You are going to need a well lit, flat area to work. A desk is a good place (go figure), and the kitchen island is a nice place to spread your maps around. Just make sure that you pick them up when you leave, or you might return to find a splotch of spaghetti sauce smeared over the Halian Mountains. Do not work in direct sunlight, for the paper you are working on will reflect so brightly as to strain your eyes. 

The research: 

Look around. There are many fine maps in many fine books in many not so great book stores. If you like someone's style, memorize the way they form their mountains, trees, rivers, and whatnot. Remember that imitation is the highest form of respect, and is not something to hide from. You will find that after a few tries at your first maps, you detect a sort of style all your own. Work with it, it will help you learn. Try to draw someone else's maps in your own way, and see how it turns out. I recommend the maps by J.R.R. Tolkien (the original ones, by either he or his son Christopher). If you look around, you will undoubtedly find something by Shelly Shapiro. These, being fairly rudimentary maps (no offense, but it's true), are easily improved on. Read through these sections of this page for notes on certain styles: Rivers, Forests, Mountains, Hills, Valleys, and Fells, Swamps, Miscellaneous Landmarks: Have fun with it.