This will be for if you are right handed. If left handed, reverse the hands.
Prepare new pots with enough new growing medium in the bottom so when old rootballs are placed in the pots the plants should be at or close to the proper height.
It is best if the soil the plants are in is slightly dry and pulling away from the edges of the pots. The rootballs will slide out of their pots easier.
Pick up pot with left hand. Place right hand on top of the soil with the main stem between your index finger and next finger.
Turn pot/plant upside down.
Tap the edge of the pot on a counter top, table, workbench or something similar mostly holding the pots with your left hand and holding your right hand just under the plant/rootball with the main stem between your index finger and next finger so as soon as it slides out of the pot you will be holding it.
The plant and entire rootball should easily slide out and then be securely resting in your right hand.
There may be some loss of soil. That is OK. If the soil is loose and not filled with roots around the edges, or only has a few small ones, do not be afraid to lightly crumble some old soil from the rootball so the roots will have more of the new better growing medium to grow/live in.
If the rootball shows signs of being root-bound, many tightly wound roots circling the pot, take a razor knife or razor blade or a very sharp knife and make shallow cuts into the rootball, a half inch to one inch, up and down the sides and back and forth across the bottom. Root-bound plants will be slow to push out new roots into fresh soil and will tend to continue to grow in a root-bound state. Each cut root will branch off in two, just as if you pruned above soil growth, and grow down and out into the new fresh growing medium.
Place in new pot/new growing medium. If the level is right fill in around the sides of the pots with the new growing medium. If the plants are to high in the pots, remove the plant and remove some new growing medium from the bottom. If the plants are to low in the pots, remove the plants and add growing medium to the bottom.
Water well so the new growing medium settles and there are no air pockets or passageways for water to run through without first saturating all the soil.