You can pick UP TO TWO main professions:
Alchemy
Blacksmithing
Enchanting
Engineering
Herbalism
Inscription
Jewelcrafting
Leatherworking
Mining
Skinning
Tailoring
In addition to main professions, there are three secondary professions, they don't have limit how many of them you can learn:
Cooking
First-Aid
Fishing
Learning skills, as well as profession recipes, is done via trainers. You can ask for city guards for directions. Some recipes can be found from vendors, or as random drops from mobs.
In WoW there are few ways to increase movement speed. Primary method being mounts. Secondary is class specific skills, such as hunters' Aspect of the Cheetah/Pack, which offer weaker movement improvement, but can be useful in many ways.
First mount, and training comes available at level 20. You get a mail from raiding trainer inviting you to buy training, and a mount. This costs less than 6 golds all together, may have been below 5 gold, but I'm playing it safe here. This mount increases your movement speed by 60% on ground.
Second mount training comes available at level 40. You get a mail once again. This time training and mount costs together something like 50-60 gold. This mount increases your movement speed by 100% on ground.
Third mount training comes available at level 60.You get a mail once again. This time training and mount costs together something like 200-230 gold. This mount increases your movement speed by 160% while flying, 100% while on ground. You can only fly in Outlands and Northrend. To fly in Northrend, you need to pay 1000 gold for Cold Weather Flying, which comes available at level 77.
So some beginner help:
I recommend getting at least mining or herbalism for gold. They're both good gold for new players. Once you know the game better, you can consider how to deal with other characters' professions.
Though, for your Warlock, I'd recommend getting Tailoring as one profession. Materials for it are easy to gain, and cloth classes can be pain if you don't get hold of Intellect gear.