First of all, I am the FIRST person to find this, so if you post it give me credit. Also, you usually aren't gaining anything because you have to recycle everything you have except for one member animal and the somehow get rid of the gems... anyway, here are the steps.
1: Have a Member account, preferably not your main account.
2: Send away all your items to another account.
3: Recycle every animal you have except for one Member animal.
4: Use all your gems to buy items and send them to another account.
5: Wait until your Membership runs out and log in.
6: It should offer to let you choose 2 nonmember animals, as usual, but since you don't have any, you have to buy one, but you don't have any gems!
7: Click the button to buy an animal and this should pop up
See how the price tag says "Free" although it is red? Now just click "Buy" and you have a Free animal!
8: Now more glitches! The screen will tell you to select the animals you want to keep. When you click your free animal, nothing happens!
9: Now you have to log out, and then log back in. Everything should be normal, and you can keep your free animal!
What do you think of this? Tell me by commenting!
Jam On!
~Geckoguy