I had the opinion that I should be able to perform well, submit my resume, and get where I want, without having to resort to other tactics (using "connections" and the like). Am I completely delusional?
At the very least, you should probably mention to your boss that you're looking to switch; if another manager comes to him and blindsides him with "hey, bobobobo put in a request to switch to my team, what can you tell me about him?" he's not necessarily going to be happy that he's hearing about it secondhand, and he's not going to be as prepared to answer as he could be.
Usually in this situation, I would probably sit down with my boss and say "I noticed there's an internal posting for < X >. I think that'd be a good move for me; do you agree? Is there anything I can do to improve my chances for getting the position? If I were to switch, is there anything I would absolutely need to wrap up before I transferred?"
My thought is that most of these requests are going to gate through him first, so you want him in your corner. At the very least, you want to make sure that he's not preventing you from moving.
(There's an "Ask A Manager" post from a while back where the manager flat-out refused to let an employee switch; when pressure was put on them, they said "fine, they can switch, but not for 3-4 months". Eventually the employee had to threaten to quit and apply as an outsider before higher-ups stepped in and forged a compromise. I'll try to find the link.)
EDIT: Link to original story and link to end-of-year update.