Once you have your CAS, and any other supporting documentation (finances, etc.), You'll have to submit the online application, schedule a biometrics appointment, mail any documents, and then wait.
If you use the Priority/Premium Service, you can have your Tier 4 visa in as little as 1 day.
I used Priority service in July 2010, and it was about $150 then. I believe it took 2 working days for the visa to be processed and issued (I used next day delivery when I posted it on a Friday afternoon). However, the visa was issued incorrectly (validity dates), and that took just about a full month to get sorted out.
you MUST apply from the country in which you are normally resident. Although you're already here, you're on a tourist visa, which unfortunately prohibits changing into any other category.
best of luck.