Welcome to the world of do-it-yourselfers. Anyone who has replaced their own tubes and tires has popped a tube, many (including myself) have done it a few times. There are many reasons this happens. Your rim tape (keeps the tube off the spoke nipples) might be bad or have shifted, you might have pinched the tube under the tire, a piece of glass or metal might be stuck in the tire, and cut the tube as it was inflated.
Here is how to change a tube.
Remove the wheel, with tire levers remove the tire and pull out the old tube.
If you are installing a new tire, its a good idea to replace the rim tape, which shrinks and/or deteriorates over time. If you don't want to change it, make sure the tape covers all the spoke nipples are covered, and that the stem hole is centered in the hole in the rim tape.
Put on one bead of the tire. Open the valve stem to let in a little air into the tube, this will make it easier to fit into the tire. Insert the stem in the stem hole in the rim, put on the nut on the stem if you are using a Presta valve.
Tuck the tube into the tire all the way around, making sure the tube is not twisted or kinked. Then push the tire bead onto the rim. Start on the side opposite of the stem, and work toward the stem. When you get near the valve, loosen the nut until it is near the end of the threads and push the stem into the rim so the bead has more room to squeeze around the rim and stem.
Check to make sure the tube is not stuck anywhere under the tire bead. Check to make sure the stem is straight, if it is coming out of the rim at an angle, pull the tire one way or the other until it is straight. Screw in the nut, but not all the way, leave about 1/4 of an inch or so between the nut and rim.
Inflate the tire enough to make the tube fill the tire. then look at the tire where it is close to the edge of the rim, there is a small line which goes all the way around the tire. Pull on the tire to make sure this line has the same clearance (around 2 -3 mm) from the rim all the way around.
Inflate the tire to full pressure, slowly. Check the tire for high or low spots, make sure the line around the bead is uniformly spaced from the edge of the rim. Tighten the nut on the stem a little snugly, but not too tight.
Reinstall the wheel, check and adjust your brake pads/calipers as necessary.
Go out and ride.