Propagating home citrus is not quite as simple as planting a seed and waiting for the new tree to grow. Some varieties of citrus do not produce "true seed," meaning the seed does not grow or will not produce the same fruit variety as what grows on the original tree. The only sure way to propagate citrus is by budding or grafting a branch from a tree with the desired fruit onto a new tree. Not all budding will take, so several attempts may be required.
Find a healthy tree with desirable fruit, and locate new growth just behind the previous season's growth. This is the most desirable budding wood available. Collect a piece of this scion wood that is around 12 inches long and contains at least two buds during the dormancy season for the tree. Wrap the scion wood in a wet paper towel and leave it in the fridge until time to graft.
Make a vertical cut onto the rootstock that is 1 to 1 1/2 inches long and goes completely through the bark. Twist the knife gently in the cut to open up the bark.
Cut a section off the scion wood that is 1/2 inch below a bud and ending 3/4 to 1 inch above a bud. Make a horizontal cut about 3/4 inch above the bud to break the bark. Cut all the way down the bud to remove the bark along the length to leave a shield-shaped piece.
Make a cut at the top of the vertical cut on the rootstock plant and slide the shield-shaped bud piece into the two cuts so it is under the bark.
Wrap the bark with a piece of budding tape to seal the wound. The bud should heal in 6 to 8 weeks if you take it in the fall and 3 to 4 weeks if you take it in the spring. Remove the grafting tape once the wound is sealed.