Do not break up the soil around the rootball, try to keep it as intact as possible and then place it into your new pot. I would have both sets of soil moistened too and make sure you give it a good soaking once a week.

They'll need a pot that's at least 2 foot diameter aswell as wide, they'll want poor alkaline soil and very well drained too.
They like a full sun position and if you're potting it you will definately need to take it into a conservatory for the winter.

I have one in my front garden, it's sheltered and south facing and it's come through the past 2 cold winters without a problem.

Use John Innes No. 2 as compost, they prefer soil based, mix it with multi purpose for lightness if you want, and what size pots are they in right now? Pot on to something that's, say, a third again as big as the ones they're currently in - you don't want them too heavy because you'll be moving them come autumn to a sheltered place. Keep well watered, feed with liquid tomato food or similar weekly, starting 3 weeks after you've repotted them, stopping feeding by early to mid August, unless you are not moving them to a greenhouse or indoors or similar, when you should stop feeding by mid July at the latest. This advice assumes you're talking about Nerium (oleander)