When I first started playing WoW, I read Blizzard's page on professions but didn't completely understand what it meant in terms of how I could choose them myself. Therefore, now that I understand, I'm writing this entry so others may also understand.
Primary and Secondary - poor terms
I think my main problem was that Primary and Secondary put specific things in my mind when I hear them. Like the fact that generally in life (except if you're into Polyamory), if you have something assigned to a "Primary" slot, there are no other slots available that are also labelled "Primary". One primary. That's it. Except in WoW, where a Primary profession means it counts towards the two professions you're allowed to choose at any one time in the game.
"Secondary" on WoW in terms of professions basically means "a skill that anyone can learn in addition to the Primary professions they've selected".
Secondary Professions Available
There are three Secondary professions available: Fishing, Cooking and First Aid.
You still need to "train" in these professions as you would your Primary ones, meaning you still need to find the Cooking, Fishing and First Aid trainers (aka Physician in some areas), but they're skills you can work on right away at low levels while you're deciding what Primary professions you want to commit to.
Committing to Primary Professions
The commitment to your two chosen Primary Professions gets to be more serious as you advance them. You cannot switch Primary professions and still maintain the old levels you had trained up in the previous Primary professions pairing, so it's a good idea to really THINK before you commit to your Primary professions.
I've heard that Alchemy, Leatherworking and Herbalism are good Primary skills to engage in, but of course it depends on whether you're looking to collect/create things to sell or whether you're looking to create things for your own use within your class specialties.
Personally, my Troll Hunter is Skinning/Leatherworking and my Gnome Mage will be a Herbalist/Alchemist once she's a little bigger.
Conclusion
If you're looking for something to do at low levels instead of just hacking and slashing and questing, find Cooking, First Aid and Fishing trainers to get you started on your way. You can fish in almost any puddle you run across, humanoids drop linen for your creation of bandages, and as your Cooking level advances, you can cook most of the fish you catch, which provides for healing and pet food.
Give it a go!