Most decent bike shops will give you instructions on how to change a tire. You should ALWAYS carry a tube (that will work on your bike); tire irons, a patch kit in case you get multiple flats; and a way to pump up the tire whether it is a co2 cartridge kit or if it is a pump that fits on your bike.

I've even had a flat on a 5 mile trip to work so no trip is too short to carry your stuff.

Don't just let them show you how to change the tire tho. What will happen is you will go out thinking you know how and then you will not be able to do something on the road. Go home after being shown how to change your tire. Sit in the living room or wherever and practice 1. getting wheel off of bike (both wheels they are different), remember to loosen your brakes or disengage brakes on a mountain bike 2. taking off the tire and removing the tube 3. putting the tube back into the tire; 4. pumping the tire back up; 5. if you are using co-2, go ahead waste a cartridge to make sure you can use it on the road; 6. put the wheel back on the bike 7. don't forget to check your brakes before you ride (either reattach them on a mountain bike or put them on the tight setting on your road bike.

It is really important for your safety to know how to do this! I wish I could do a video (no video camera ) instruction and put on this site. I have given instruction on this many times!