Here are some tips from apartmentherapy.com:
What You Need
Materials: Fresh potting soil; a bigger, clean planter; scissors (to cut plastic planter if needed); spray bottle filled with room temperature water and a few drops of plant food; waste basket.
Equipment: I prefer re-potting plants in my kitchen sink. Be very careful not to allow a lot of potting soil to go down your drain. Potting soil is easily cleaned up when dry but not as easily when wet.
1. In this example the roots have grown out past the pot and the plant is “pot-bound.” The first step is to carefully cut off the old plastic pot without damaging the roots. Cutting down the side of the plastic planter works well. If the pot is not plastic, turn the plant upside down and very carefully and slowly jiggle the roots out.
2. Once the plastic side is off, tackle the bottom. Use scissors to snip through the plastic in many places until you can easily remove it.
3. Make sure the new, larger pot is clean by using a touch of bleach in water so you do not transfer any plant diseases. Rinse very well. Also, it is important that the new pot not be too much bigger. A planter that is too big can hold too much water causing root rot or can inhibit the top of the plant to grow until the roots have filled the pot. Always choose a pot with drainage holes.