The first thing to remember when asking yourself 'How do I replant my orchid?' is that orchids definitely need to be re potted every 18 - 24 months. This of course can depend on your plant and size of the current pot but regardless of this I would never wait more than 2 years to replant your orchid. This will ensure you are giving it maximum care and making it as healthy as possible.
The main purpose of replanting your orchid is to provide fresh media (soil/bark etc.). This will give your plant new media to grow in and ensure that it keeps flourishing. Doing this will mean that the orchid has fresh food and will continue to flower and mature, which is when they are at their most beautiful.
The type of pot isn't so important as orchids can be potted in either plastic, clay or decorator pots. The type of pot the plant is in can effect how often you will need to water, so keep an eye on this the first few times. Make sure you always use pots with drainage holes, orchid roots should never be sitting in still water because they may rot and die. Not Good!
Some people will replant their orchids on whim. This is not a good idea. Orchids are delicate flowers and should not be replanted without a compelling reason. This is the most important tip I can give you about How to replant and care for your orchid. The old mantra of, 'if it ain't broken don't fix it' definitely applies here.
Orchids like to be very snug. A small plant in a big pot means that all the orchids effort is taken up in trying to build a larger root system and it will not flower properly. Make the pot snug, but not too snug.