Basically, you need a spare tire (two is better, since you've got presumeably got two wheels and/or may flub the first change), something to help you get the tire off the rim (tire levers), and something to pump it back up with. (A CO2 cartridge system or a pump.)

If you use CO2, carry at least two cartridges. (The likelihood that something will go wrong with the first increases in inverse proportion to the number of spares you have.)

If you choose a mini pump, make sure you can actually use it to pump up a real live tire. (I personally once purchased a fairly highly-rated mini pump that even my 230 pound lumberjack of a husband cannot get my tires up to a reasonable pressure with. )

I do not recommend patches except as a backup system. I have both heard about and been involved in too many marathon tire-patching sessions that did not end well. You want to get home while you still have your natural teeth. Bring tubes.

If you need more information, go to the bike store and ask the nice salespeople what you need. They're all pretty good folks around here and will help you out, and most will not try to sell you too many large farm animals you don't need. Okay, maybe a llama, but that's only fair, really. It's like asking a kitten not to toy with a grasshopper.

Whatever flat kit you get talked into...er, choose to employ, it's a great idea to try it out in the comfort and relative calm of your living room before the real moment of truth arrives. That said: if the whole tire-changing thing wigs you out, don't stay home because of this; come on out on one of our rides with your supplies, and if you flat, we'll help you out (and show you how to do it yourself next time.)

Btw...Great Escape on Laurens road offers free tire-changing classes for women periodically. These are given by Debbie, who is amazing and will make you want to become a bike mechanic too. They give you your own tire to actually go through the entire (ark, ark) process on, which makes it way the heck clearer than reading about it on the internet, let me tell you. Give them a call and ask when the next one will be. Or, if you and/or several of your friends are interested, let me know; they're such nice folks they've offered to do some for us 'specially on request.