At Langara they'll have you reading the "practical Chinese reader". It's decent but a bit outdated (in the dialogues the characters call each other "comrade", but the meaning has since shifted to mean "homosexual"), so take it with a grain of salt. In my opinion, its decent enough so just get a copy of the book from the Langara bookstore and learn it by yourself. It comes with an audio CD so you can learn how the morphemes sound. Listen to it religiously. Every second of free time that you have you want to be listening to it.
Just work through the first couple of book at your own pace. When you get through the first couple of books, you'll have the basic gist for how Chinese grammar works. You'll understand the stroke order for writing characters (and have a couple hundred characters memorized). At this point you want to memorize the 214 Chinese radicals. Radicals are the components that make up characters. This part (in my opinion) is really boring, but you have to do it if you want to be able to use a dictionary/learn new characters quickly and efficiently.
The next step is to start listening to Taiwanese radio. I focused on news but you can find radio programs on all sorts of topics. You can download podcasts in the iTunes store. Start listening to them religiously. At the start you'll have no idea what anybody is talking about, but just keep doing it, your brain will get in tune with it.
In my opinion, the next step is where you want to get a tutor. Get a bunch of Chinese magazines or newspapers (or poetry, or literature)from the library (whatever matches your interest really). Get the tutor to go through one article per session. When I did this I paid for three hour sessions, and had the tutor go through one article per session. Then I'd take my notes and study them for a couple of days. This step is important because you'll learn lots of important vocabulary that you wouldn't learn in textbooks. Note, that quality instruction is not going to come cheap, but it's necessary if you want to become functionally competent.
After that, start making Chinese/Taiwanese friends.
If you do this for a couple of years you'll really tune into the Chinese language.
Good luck!