Method: I use USPS Priority 2-4 day or USPS Priority Express 1-2 day shipping. If possible I will also use Speedy Deliver as they are cheaper.
Box: You can get a Priority box online or at your local USPS shipping facility. Speedy- at least my local facility- excepts plain boxed which you can purchase at places like Walmart. Use the smallest box possible as they will be cheaper to ship.
Marking: Write any important information on your box. Examples: Live animal(s), live plant(s), handle with care, extremally delicate (or fragile) , keep out of direct sunlight, keep in cool spot, this side up, keep in warm spot, etc.
Lining: Tightly line the box with foam. You will need a piece for each side, the bottom, and the top of the box. You can find the foam at your local shipping facility, or online. You can also find insulated boxes at your local pet store- and they will normally give them to you for free. Foam with a reflective foil like side will also be handy. If its hot out, have the reflective side out the outside to reflect the outer heat, if its cold have the reflective side on the inside to reflect to inner heat.
Padding: you can use newspaper, packing peanuts, packing paper, or bubble wrap to fill the extra space in the box. This will prevent moving and damage of the contents.
Packing Aquatics: Use as small of a bag as possible. Preferably, the fish can easily turn around in it. Make sure there is enough water so the fish is covered whichever way the bag is turned. Use 50% new conditioned water and 50% aquarium water. Add some stress ease to the bag, and optionally a small piece of Indian almond leaf. For every 1 parts water, have ATLEAST 2 parts air. You can use pure oxygen if you wish but it is not necessary. Do not fill the bag with your exhaled air. Double knot the bag off, then tightly tie below the knot with a rubber band. You can get bags at your local fish store or online. Use as thick of a bag as possible ESPECIALLY if you are shipping a prickly aquatic to prevent leaks. For plants, use the same process but instead of putting water in the bag put in some very damp paper dowel. Once you have bagged your fish once and properly sealed it, repeat the process. This time though, put the bagged fish into the second bad upside down. This will push in the bags corners in and prevent the contents from getting trapped and squished in the corners. Fast live aquatics 2-3 days before shipping.
Packing Non Aquatic Small Exotics: Use as small of container as possible. Depending on the animal and size, use a dish and lid or a deli cup will air holes drilled in it. Preferably, the animal can easily turn around in it. Put a soft rag, the animals bedding, or unscented paper towel on the bottom. For every 1 part the animal takes up, have ATLEAST 5 parts air. Make sure the container is tight so the animal can not escape. If possible for your species, fast your animal for at least 12 hours before shipping.
Heating & Cooling: If it is more then a few degrees out of your exotics proper temp where you are shipping through, you will need to apply temp change methods. If it is to cold, use a small animal shipping heat pad. If it is to hot, use a small animals ice pack. You can find them online. Do not wrap the heat pad in anything. You can wrap the icepack is a small layer of paper towel to absorb sweeting unless instructions say not to. Put the heating or cooling pack on the top of the box before the top lining foam.
Process: Line your box, pack your animal, place the animal in the middle of the box and put padding all around it, add in your heating or cooling method, tape the box up, label it, put the addresses on it, ship it out.
Cost: Shipping in total cost around $10-$25 on average in my experience.
Have fun and enjoy your new option!