I dissolve the priming sugar in 2 to 3 cups of water that has been boiled. The boiling sanitizes the kettle being used. Northern Brewer has a good carbonation calculator for different types of sugar which can be used for priming.
I begin the racking from the fermentor then add the priming sugar solution to the bucket. Avoid any splashing which can add oxygen to the beer. The end of the siphon tube is flat on the bottom of the bottling bucket and curled around the base of the bucket. This creates a gentle swirl as the beer is siphoned. The swirl will mix the priming solution throughout the beer.
Bottling should begin immediately to limit the time the beer is exposed to the air at the surface in the bottling bucket.
The temperature to use in the calculator is the highest temperature the beer fermented at, or rested at, after CO2 production by the active fermentation has ceased. This helps determine how much CO2 remains in solution. CO2 leaves solution faster at high temperatures than lower temperatures.