The main strategy for the zero facts is to avoid arbitrary rules and instead stress the meaning of multiplication. The commutative property should also be emphasized.
For example, 0 X 6 means 0 groups of 6. Flipping the fact around, 6 X 0 means 6 groups of zero. When playing a game like circles and stars, a dice can be made that has zero as one of the factors.
An activity using the students can also emphasize this relationship. Have the students stand in groups of 6. Now stand in groups of 5. Now 4. Now 3. Now 2. Now groups of 1. Now groups of zero.
The commutative fact can be demonstrated having students work with counters. Have students 5 groups of 6 with their counters. Now 4 groups of 6. Now 3 groups. Now 2 groups. Now 1 group. Now 0 groups.