If you are growing Tulasi devi in a pot, naturally she will eventually outgrow it and require a new, bigger pot. If done properly, transplanting Tulasi devi into a new pot is quite easy and Tulasi devi will flourish with her new space. If the roots are starting to grow on the surface of the soil or are coming out of the bottom of the pot, these are signs that transplanting needs to be done.
The first consideration is the size of the new pot. The pot should be about two inches bigger in all dimensions, and should be made of clay with a hole at the bottom for drainage. Clay pots are porous, allowing moisture and air into the soil, which is good for the very small branches of roots at the outside of the root structure. They also do not change temperature as quickly as plastic, helping keep the roots warm. Finally, by Vedic standards, pastic is contaminated and mode of ignorance. If Tulasi devi is put on an alter (especially at a temple), clay is highly preferred for this reason. Too big of a change of pot can cause problems in watering, as the roots will not expand into the new soil fast enough, resulting in potential mold growing in the outer layer from that soil remaining moist longer while the rest of the soil dries quicker. Too small of a change will result in Tulasi devi needing to be transplanted again too soon, which won't give her enough time to recover from the shock of being transplanted.
The next thing to consider is soil. As stated in the "Planting the Seed" page, any soil with animals products must be strictly not used. The soil I have always used is called "EarthGro", and I combine it 70% soil, 15% perlite, and 15% diatomaceous earth. This combination works very well at retaining moisture while allowing air into the soil and is not too heavy.
Once these two things are in order, the first step is to water Tulasi devi. This should be done a few hours before transplanting so that the roots will stay together nicely when she comes out of the pot. Then, the new pot can be prepared. The hole should be covered with a piece of clay, and then enough wet soil put into the pot so that when Tulasi devi is put in her stem comes to about 1.5 inches below the top of the pot. Tulasi devi can then be taken out of the old pot by being held upside-down and pushing her out from the bottom hole. Two people make this much easier to do. Once she comes out, place her in the new pot and put more wet soil around her until the soil is level with Tulasi devi's stem. Remember to leave space at the top of the pot for watering. Do not pack the soil too tight, as this can cause watering issues. After all of this is done, simply water her and pray that she does well in her new pot.