The hardest part is removing the tire from the rim and putting it back again. If you can get the hang of doing that, you'll be fine.
If you want to patch the tube, try inflating it, then running it through a bowl of water. In a pinch, you can sprinkle water from a bottle over the tube. Look for bubbles, or the sound of air to find the hole, then patch it. Remember to dry it first.
Look for the thorn or glass in the tire that made the puncture and remove it before replacing your tube.