Let's start with a new character. What I do is choose 2 gathering professions for the first 20 levels. You can change professions at anytime. What this does is allow you to make extra gold that you will need to become an enchanter. Typically, I choose Herbalism and Mining. Both will allow you to generate nice amounts of cash. Once you reach level 20 or so, (can be more, can be less), drop one of your professions in order to add enchanting. Which one you drop is entirely up to you. As you level your character, mining gives you toughness and herbalism allows you to have lifeblood, both come in very handy.
Once you have picked up enchanting you will need to do a few things to get ready. Hit the auction house and purchase approximately 200 Strange Dust, 100 Lesser Magic essence, a cheap bracer (or use your own) and 1 copper rod. This will get you started. You will need other mats, but that can wait for the time being.
Make your ruined copper rod and start enchanting. Enchant you bracer over and over again with "Enchant Bracer Minor Health". Keep going until you have reached level 75 then visit the enchanting trainor. Now you are at 75/150 in your enchanting skill. Resume enchanting Minor Health until you reach level 90, at which time it turns green and becomes harder to level with. Now, go to "Enchant Bracer Minor deflection" until you reach level 100. From there do "Enchant Chest Absorbtion" until you reach level 110. Then "Enchant Bracer Minor Stamina to get to level 120. You may want to train again at this point. Continue on this way until you are bored to dealth, lol. Just remember to do the enchants that will take the least amount of materials as possible. They do get costly! Once you reach level 150 hit your trainor and the Auction House again. Look for new enchanting recipies you can afford, as well as new mats you will need. Some of the mats you will need are Soul Dust, Vision Dust, Greater Magic Essence, Greater/Lesser Astral Essence, and some various shards. Look at your enchants to see what material will be needed.
Another thing you will want to do is get some Armor Vellum & Weapon Vellum. These will allow you to do enchants on scrolls to sell in the Auction House. If you are in a guild ask for an Inscriptionist to make them for you. Otherwise, it's more money into the Auction House. The scrolls are a great way to make money with your new profession, and an awesome way to level your skill. This wasn't available when I created my first enchanter and, let me tell you, it makes leveling so much easier!
Now you are on your way to becoming a real Enchanter! Well, not real, it is a game. Remember, scrolls will be your best friend. Make sure you use this to your advantage. That's where you will make your best money.