1. The first person decides where the first apple would be cut, such that he would be equally happy with either taking the larger portion or dividing up what remains.

2. The second person either says he wants that larger portion, in which case he's done, or he says he wants to divide up what remains, in which case the first person takes the larger portion and is done.

3. The third person decides where the second apple would be cut.

4. Either the first or second person (depending on the outcome of the second step) picks either the larger portion of the second apple or the two smaller portions.

5. The third person takes what remains.

6. The two apples are cut and their pieces distributed.

This doesn't guarantee a solution, since it's possible that the third person would have wanted the larger portion of the first apple. It only works if we assume that the first person, when given the motivation to cut fairly, does so with high precision. Otherwise the first person can, by screwing himself over, also screw over the third person.