Let's get started. First when you are done with your lemons save your seeds, wash them in plain water. Then just in a paper cup, place your seeds in sterile soil. After planting keep the seeds watered and covered with plastic to hold in the moisture. You can use a plastic cup also, but make sure to put holes in the bottom of the cup for drainage.
Also if you want you can germinate your seeds in a paper towel. Take three paper towels and place on top of each other and moisten them. Then you want to fold them in half, and in half again. Put your seeds in the middle and keep folding for maximum coverage.
Always keep your paper towels moist, by putting them on a plate that will let you add additional water to it. Or put your paper towels in a baggie, this will also keep them moist. If you do use the paper towel method make sure you keep the towels away from sunlight, but yet keep them in a warm spot. You don't want them near a heat source of any kind, for the paper towels will dry out.
You can transplant your seeds to a paper cup with soil when you see small roots and leaves starting to form. When you transfer them make sure you keep the leaves just below the soil. Then you can put your plant in sunlight. You don't have to worry it will take some time before your new plant out grows it's paper cup. When it has you want to get a container twice the size before transplanting. Make sure after that, you do not over water.
Just sit back and watch your lemons grow.