You do need certain tools that's for sure. First get a good set of irons not cheap plastic ones, I've seen them break. Soma steel core irons are the best, see:
http://www.biketiresdirect.com/product/soma-fabrications-steel-core-tire-lever?utm_campaign=products&utm_source=bestwebbuys
Then to make tire removal and installation faster you should also consider, as an option, the QuikStik, see:
http://www.rei.com/product/546083 this thing once you got the irons started at removing the tire you slip the Quik Stik under the bead and just follow the rim and the tire comes off.
You obviously need a good pump, Topeak Morph and the Lezyne Pressure Drive are probably the best pumps on the market. Don't rely on CO2 inflaters, sure their fast but you can run out of air on the road, with pump you have unlimited air; also with CO2 you have to keep buying carts and tooting back your garbage, yuk who needs that ****?
You need to learn how to fix, and by fix I mean PATCH a tube on the side of the road, it does not take longer; I can patch a tube using glueless patches faster then putting in new tube. Hows that you scream. First there's no need to wait for glue to dry to apply the patch with glueless patches; second I don't have to remove the tube just pull out about half of the tube where the hole is making sure the hole is in the center of the half; third I don't have to hassle getting all the air out of a tube to stick it back into the saddle bag! I use Park Glueless patches because the work fast, work great, last forever, no glue tube to dry out nor have to wait for glue to dry before putting a patch on. You simply buff the tube lightly in an area slightly larger then the patch will cover as you would with a glue on type, then remove the patch from the backing and press on very hard between your thumb and index finger for about 30 seconds.
You need a spare tube just in case your main tube is damaged beyond repair, or it's raining and you can't get a patch to work. Keep the tube in it's box so other things in the seat bag won't puncture it. I buy ultralight racing tubes because their more compact. I have no problems rolling up a tube into a size of a hockey puck but it does take time.
You should carry a mini tool. I like the Park MTB3 but there are other good ones besides that one. In that tool is a knife you can use to dig out debris in the tire. Also a cheap real small folding pliers is great for pulling things out of tires (also great if you need pliers), but I can usually pull stuff out with my fingers.
Once you remove debris from the tire that caused a flat, you may have to put a (Park) Tire Boot over the hole from the inside of the tire if the hole is large. Just cut to fit the hole.
In that vein you should carry a tube of SuperGlue, because once you take debris out of a tire that caused a flat you can use the glue to fill in the hole from the outside.
I had a 1/4th inch cut in one my tires that did not penetrate the cords, but I sealed the cut with SuperGlue, then to be safe I cut a tire boot about 1/4th an inch by 1/2 inch and placed it under where the cut was.
You also should carry some GoJo cleaning pads in sealed pouches so you can clean your hands thus any dirt and oil won't get on your clothes, handlebar tape, hoods etc. also alcohol pads in case you need to clean the tube after you buffed it before you apply the patch.
Cell phone just in case, but I haven't had to use it because I can fix most anything on the road and my wife is my wife not my mommy, so I'm not going to call her to come get me because I've had a flat!
Practice fixing flats at home over and over and over till your confident enough to do it on the road.
Option, most will blast me for this, but I like to ride into remote areas that can be as much as 60 miles from home. So I carry a 180 grm ultralight folding racing tire, that I've folded very tightly and bound with rubber bands to keep it tightly folded in my expandable wedge seat bag.