Water the plant that you plan to repot heavily for at least a couple of days before you perform this task. This will soften up the soil in which the plant is originally potted which means it will be easier for you to remove the plant from its original pot.
Hold the plant’s stem as close to the soil as possible and turn the pot upside down. Firmly tap the pot at its back and carefully pull away the pot. You might have to cut around the soil edges or break the pot if you are facing difficulty removing the plant from its original pot. There is no need to worry if you end up breaking a few roots in the process. As a matter of fact, cutting around the edges of a root-bound plant is required to enable the roots to branch out in the new soil in which you repot the plant.
Carefully scrape off about one third of the soil that came up with the plant to reveal some of the roots.
Make sure that the new pot base is around 1 inch larger in circumference than the old pot. Add a few inches of potting soil in the new pot, carefully set the plant in it and add more soil until the level of the soil is at the same point where it was in the old pot.
Add soil around the root ball and tamp it down hard with the tips of your thumbs or fingers. This will ensure that there are no air pockets that can become a possible cause for the roots of the plant drying out.
Just to be sure that the roots are properly set in the new soil, thump the new pot against a firm surface. Be careful because you might end up breaking the pot if you thump it too hard.
Start watering the soil and continue until water drains out the bottom of the new pot. Let the soil drain and place the pot in a suitable environment.