Purchase your new pot(s) and quality soil. DO NOT pick a pot size under 4-gallons. 5-gallons or more would be better, I normally use 7-gallon pots, but 4-gallons is as small as you can go unless you're growing dwarfs or something tiny and still have adequate space for a healthy root system.
Put a layer of new soil in the bottom of your new pot(s)m gently compacting it.. Set the old pot/plant inside to see if you have roughly enough soil so when the old root-ball is placed in the new pot the plant will be at the right height.
(From now on the instructions are for a right handed person. If you are left handed, reverse the hand instructions)
If the soil in your old pot is slightly dry and pulling away from the sides of the pot the root-ball will slide out easier. If not you can run a long knife around the inside of the pot making sure the blade is scraping the pot and not the roots.That will help loosen the root-ball from the pot.
Pick up the old pot with your left hand. Place your right hand over the soil so the main stem is between your index finger and next finger. Turn the pot upside down while mainly holding it's weight with your left hand and with your right hand just barely touching the soil.
Tap the edge of the pot on a counter top, work bench tabletop or something similar. The plant and root-ball should then slide out of the pot and be securely resting on your right hand, main stem between index finger and your next finger. There may be some loss of soil, but that doesn't matter, even if it is considerable.
Inspect the root-ball. If the roots are out to the edges of the root-ball and tightly wound the plant is root-bound. If so take a razor knife, a single blade razor blade or a very sharp knife and score the root-ball making cut up and down the sides of the root-ball about a half inch to an inch deep and about every three or four inches apart. Also score the bottom of the root-ball in a crisscross pattern and again making the cuts about a half inch deep to one inch deep. A root-bound root-ball will continue to grow in a tightly wound mass rather than pushing out roots down and to the sides into fresh soil. Scoring the root-ball (cutting roots) works like pruning above ground growth. Where each cut is made the root will split off into two new root tips and they will push down and out in search of space and fresh nutrient rich soil.
Place the root-ball/plant into the new pot. If the plant level is correct fill in around the old root-ball with new fresh soil. If the plant level is low, remove the plant/root-ball and add more soil. If the plant level is to high remove the plant/root-ball and remove some of the new soil. Then fill in around the old root-ball with fresh new soil.
You want to make sure there are no air pockets or passageways for water to pour through to the bottom of the pot and out the drains without adequately moistening all the soil. If your old root-ball remained more or less intact you can use your hands and gently compress the new soil around the sides of the old root-ball and then water well giving it a good full soaking.
If you had a fair bit of soil loss from the old root-ball and had many loose dangling roots you do not want to push on and compress the soil because you may break the loose roots. In a case like that give a good full soaking of water to compress the soil. If after doing so the soil has sunk some, add more soil to the top and water again, but not as heavily. Just enough to compress the additional soil.
Let drain well.
Smart Pots or Rootmaker Pots or ny of the air root pruning pots are good. They create very healthy root systems and very healthy root systems create healthy vigorous growing plants. Just because they are air root pruning pots does not mean you can buy smaller pots than you would otherwise need. The roots will still need adequate space. But using air root pruning pots, of an adequate size, along with using quality soil, is the simplest thing anyone can do to have a happy healthy root system that the above ground growth will be thankful for and will make use of.