Repot procedure:
1. Wait until at least a week has passed since last watering, Plants needs to be under watered at this point , for 3.
2. Prepping the soil(a mix of gravel, perlite, coarse sand and soil).
3. Cleaning the roots, eithet by carefully tapping, brushing and shaking off the soil off of them, or wet cleaning them with whatever you can pressurize.
This is important for plants with gentle roots, that dont take kindly to organic soil, or brushing(lithops, plants in muddy soil, etc)
4.(if wet) Wait for the roots to dry out, at least overnight. The dryer the better.
5. Pot. Plastic pots(black and usually square), filled with the same stuff.
6. Rest period-at least a week if the plant was dry. Usually 2 weeks if gentle.