After eating about 50 mandarins and clementines (not all at once!) I finally found a clementine that had 1 seed. I soaked it in rain water for a week, peeled the outer skin and planted it in my propagator. Now lo and behold, 4 days later a seedling appeared. This photo is taken on day 3 after the seedling emerged.

Congratulations. Note that Clementine seeds do not germinate true. Therefore, you will not get an actual Clementine tree, or fruit the same as the one you retrieved the seed from. In general your seed will produce a type of small leafed mandarin tree that will produce a mandarin type of fruit. Generally the chances are that the fruits will be inferior to the mother tree. On the other had there is always a chance that your seed will produce an outstanding chance seedling. Millet[

But how long will it take before they set fruit? If ever.

All citrus seeds planted will produce fruit, if the tree is properly taken care of. A containerized Clementine started by seed should produce fruit in approximately 5 years. If the tree is grown in a greenhouse that is kept warm year around, so that the tree obtains 12 months of continuous growth, the tree could begin blooming in 2 to 3 years. I have greenhouse grown four Clementine trees from seed, with the trees blooming around 2.5 to 3 years. However, even though the tree might begin fruiting at 3 plus years, mandarin varieties normally do not produce quality sweet fruit until the tree reaches the age of 5 years plus or minus. - Millet