Here are the steps to perform for a successful tube change on a front wheel with caliper brakes.
Open up the front brake to allow the wheel to clear the brake pads.
Release the quick release by opening the lever and loosening the nut till the axle will come off the safety tabs in the fork and the wheel is free from the bike.
Give the outside of the tire a visual inspection to see if the cause of the flat is apparent. A piece of glass, thorn, metal shard, etc. are all objects that may be sticking out of the tire and cause the flat.
Open up your saddle bag and remove two plastic tire levers. Place one under the bead of the tire opposite the tube stem. Place the other about six inches apart from the first.
Push both levers simultaneously and get the bead to come off the rim.
Hold one lever in place and slide the other away from the first sliding it between the rim and the bead. Do this until the entire side of the tire bead has separated from the rim.
Pull the tube out from the tire and inspect it for debris or damage that may have caused the flat.
Also check the rim strip inside the tire and make sure a spoke is not exposed.
Once you have found the cause of the flat, remove it from the tire.
Pull out the new tube from your bag and gently add some air to it to give it shape.
Remove the stem nut and put it in a safe place.
Insert the stem into the hole in the rim and then insert the rest of the tube around the rim and inside the tire.
Using your fingers, push the bead back onto the rim starting from the stem location. Make sure the tube is not pinched between the rim and the bead.
Once the bead is fully seated on the rim, pull out your mini pump from your bag.
Open up the valve on the stem by rotating the small nut and depressing the plunger. A small hiss will occur letting you know that you let out the small amount of air in the tube.
Place the pump over the stem and pull the lever on the pump to secure it to the stem.
Pump the tube up to the desired pressure and remove from the stem.
Place the wheel back into the fork and slightly tighten up the skewer nut until the lever can be closed and it takes a moderate force to close.
Re position the brakes to the riding position and spin the wheel to make sure it is not rubbing. Adjust the centering of the wheel till it does not rub.