If your plant is hard to take out of the pot (because it’s big and cumbersome, and it won’t slide out easily), try breaking the pot (if the pot is ceramic or clay) with a mallet and take it out that way, or if the pot is plastic, try knocking the sides of the pot against a hard surface to loosen the soil mass first, then gently pull the plant out at the base. Because the plant is overgrown and awkward to handle, I would lay the plant on its side on the ground (preferably outside because it can get messy) before performing the operation. Sometimes if you water the plant a day or two before the transplant, it helps to loosen the soil mass first.
Select a larger pot with a broad base to put your plant in. The pot should be ceramic or clay (not plastic), as this will provide enough “base weight” to hold the plant down and prevent toppling when the soil is dry. If the plant is really overgrown and cumbersome, you might want to trim off some of the outer leaves to give the plant more balance and even weight.
The soil you use should have some sand in it, not only for drainage, but for added weight and bulk. I find “all-peat” mixtures too light for plants, and they often get dry and matted, forming an impermeable layer when you try to water.