Hi Dexter,
Sorry to hear about your flat! That sucks. I had just bought my bike and I let my little brother give it a go around the block, and the rear tire popped before he even got ten feet from the house. Luckily I bought used so I was planning on taking it in for a tune-up anyway, so it wasn't that big of a deal, but changing a tire is a tough job if you've never done it before. I got a new set of tires, and it took me about an hour to get 'em on properly the first time I tried it. A couple of tries later though and I had it down.
There are a few indespensable resources I've found though when looking at how to replace tires.
First place I looked was at my LBS' website. Specifically, their pages on how to replace a flat, how to patch a tube, and how to inflate a tire. They get really specific, and pictures are included!
It DEFINITELY helps to have some tire levers handy. That tire is built to be stiff and stuck, so it's not going to move with ease. However, they're not absolutely necessary--it's just going to take more effort to get the tire off if you don't have any levers with you. I found a video on Google Video with just such a situation (one where no tire levers are available). It's here and here. The first one shows how to get the tire off, the second shows how to get the tire on.
There's also an excellent ViewDo tutorial on Google Video right here that shows the whole process from start to finish, including the patching.
Don't be afraid of the tires/tubes though! They're tough, built to resist hundreds of pounds of force, so don't be afraid to push and pull a little.
I'd say invest in a pair of levers though. Six bucks will get you a nice pair (at least, that's how much the steel-core ones I got cost at my LBS), and they really make the job much easier (unless you're Jim Langley, according to those videos!).
In answer to your other question, according to the website above, you probably shouldn't try patching a hole that's bigger than 1/4 of an inch. You can probably go a little bigger, but that's a safe guideline to go by--those patches are only so big, after all. A well-done patch is the strongest part of the tube once it's set, though, so do what you feel safe with.
Hope that helps! From one n00b to another 🙂