This is how i pack my plants,
1. Get ziploc bag
2. take the plant out of the aquarium
3. Put in bag
4. add very little bit of tank water, 2 tbsp if you're shipping it in the large ziplock bag.
5. Close the bag all the way.
6. Gently flip the bag upside down, swish to the right, swish to the left this is so the water gets on the plants and sides of the bag.
7. Open the bag alittle bit.
8. Gently press as much air as you can out of the bag.
OPTIONAL: Depends on how big of a box you're shipping in.
9. Put the bag of plants in another bag filled somewhat with air or add something to fill the rest of the box up so the plants don't move all over the box.
As far as live animals, I have no experience.