I have some questions about how I would go about connecting myself directly to the 'toobz' without the use of a commercial ISP, thus being my own ISP. What kind of equipment is needed for this? And how much would it cost?
There's no such thing, even ISP's have ISP's. The most you can ever hope for is that other networks view you as a peer, where your traffic is as valuable to them as their traffic is to you. See:
Well, what I mean is basically having the equipment to connect myself to the internet for free. Would it be just a server and such?
No, it's impossible
Even AT&T and Comcast pay for the privilege of accessing other servers, about the closest you could get to "free" internet is charging it to someone elses credit card, or a free month of AoL (lol)
Borrow wi-fi from your neighbor. Viola, free internet. 
More seriously: I owned and operated an ISP (and helped operate another, and consulted for others) through most of the '90s and early 00's. The kind of questions you're asking suggest to me that you have some fairly significant knowledge gaps that you're going to need to fill in over the course of the next few years if this is more than a passing fancy for you.
This isn't meant to discourage you, but until you understand the kinds of topics being debated on, say, the NANOG mailing list (substitute your regional network operators' group as appropriate), you're a very long way from being able to do what you're talking about (building a service that tier-1 providers may be willing to peer with for "free", ie. for the cost of transit; see the link posted earlier regarding peering, although that's a higher-level business/culture topic, and it appears you're still struggling with the basics).
Now, if you just want to build an ISP (dialup in some parts of the world, WISP, CLEC or other facilities-based provider, VPS/hosting, etc...you weren't exactly clear about what you mean by "ISP", which is kind of an overloaded phrase these days), that's much simpler, and will involve a connectivity arrangement with one or more upstream providers; you'll give them money, they'll give you bandwidth. Maybe. If a backhoe doesn't come along, and as long as you don't end up competing with them a little too well. 
Nothing is free.
Anyway, I meant to keep this short. I'm sure I and others here would be glad to answer questions (although this really isn't the right audience for a topic like this), but they'll need to be a lot more specific with what it is you're having trouble wrapping your head around. You might want to spend the next few months reading and learning first, though; anything related to CCNA (Cisco Certified Network Associate) certifications are a great way to quickly bootstrap your knowledge and force you to deal with your experience gaps, but any introductory networking books and classes would be useful.
(It's entirely possible that I've misjudged your experience level because of the brevity of your posts; please, do correct me if I have, and accept my apologies if so.)
Thanks logic, that cleared up something I was misled about. I have never really learned about the actual structure of the internet, just the basics and how to use it.
I'd like to acknowledge that I was actually wrong in my previous post, I should have probably realized they had deals with each other... (but it doesn't really change the fact that if Joe Smith were to form his own ISP he'd have to pay those fees)
Heh, peering is...messy. There's no real set of rules for navigating it; it boils down to mutually-advantageous connectivity (ie. as long as the amount of traffic being sent and received by each party is roughly equal, the agreement works for them). This is why I said it was more of a business or culture topic than anything else; these agreements end up being the result of hard-fought negotiation.
Every so often someone will try and throw their weight around by de-peering with the other party to prove they're serious in those negotiations (to which the de-peered party may respond by no longer sending packets to their ASNs entirely and starting a media campaign against the instigator, meaning two major ISPs suddenly can't talk to each other, and everyone loses).
Who pays the cost of transit (ie. the physical arrangements to connect the two providers; anything from connectivity to data center space), and whether/how much one party pays for the privilege of connecting to the other is all part of that negotiation.
And you're absolutely right: "Joe's Bait & Tackle & Internet" won't ever get close to those kinds of negotiations. They'll be paying for connectivity to Tier-2 or 3 providers just like everyone else, until they get large enough (or "important enough", from a traffic perspective), to sit at that table.
Even AT&T ... pay for the privilege
As one of the first companies given a class A block of addresses, I have a sneaky suspicion they don't pay very many or very much for the privilege.
The big fish...
(List of tier 1 networks)