One of the most common questions I get, after "how do I grow this" of course, is about how I ship plants. I've been shipping and receiving plants through the mail for so long, I forget that there are many people out there for which this is a new concept. But its actually rather straightforward.
The first step in hot weather is to water the plant, generally the night before packing, to reduce stress during transit. In winter when it is cold I usually prefer to ship the plant dry, to avoid clammy, cold roots. Spring/autumn can go either way. Exception: in winter when it will be below 30F both here and at the destination I generally do not ship. Some growers do ship during such conditions with either the aid of a 60hr heat pack or overnight shipping.
Next is to arrange some newsprint or glossy ads on top of the pot and tape or rubber band it down. This will keep the media and plant secure in the pot.
Then the plant is wrapped in newspaper. I usually use two sheets or one sheet folded in half for smaller plants, and set the plant on the diagonal. The sheet is wrapped securely around the pot, and then the upper portion of the plant makes a stiff, triangular package the protect the foliage.
Finally the plant is set into the box and secured with packing peanuts (and before anyone gets unhappy about my use of packing peanuts, they're always reused ones from other packages!) or more newspaper. The plant is shipped by priority mail, clearly marked as perishable.
Other details to consider: Certain plants cannot be shipped to certain states due to USDA regulations aimed toward protecting local agricultural cash crops and/or protecting the local ecosystem from invasive species. Your local USDA extension office should be able to provide you with a list of restricted items. Shipping plants outside of the USA also entails extra paperwork, I believe, so I don't do it.
Other types of plants may require other packing systems, and plants in bloom may require more creative stabilization to protect the flowering stem.I've seen African Violets, for example, shipped nicely by dropping the plant into a plastic drinking cup (after securing the plant in the pot of course) and sticking one or two short bamboo skewers through one edge of the cup to keep the plant inside. This prevents crushing of the foliage, which can be a big problem with mature African violets. Be creative, but avoid packing so securely that the recipient gets trapped by a tape octopus trying to get the plant back out.