The experts recommend disassembling your table before moving it, as moving it in one piece can crack the slate, split the rails, and cause it not to play evenly or sit level. The slate is usually screwed to the frame of the table, and moving it in one piece can cause it to crack where the screw holes are located.
They also recommend hiring a professional to re-assemble it to ensure that it plays optimally.
The slate is heavy - usually around 1000 pounds or more depending on the table. You'll need a vehicle capable of transporting at least this much weight. When transporting it, be sure to rest it vertically on it's edge, and NOT laying flat. (risk of cracks)
Avoid using "pool table dollies" as shown below, as they are VERY bad for the table. Basically, the entire weight of the table is supported by one rail, which is obviously very bad.
So in short, if you must move the table yourself rather than hiring a professional, you'll want to disassemble, move the parts, and re-assemble at the new location.