As everyone has their own techniques for re-potting, you will find what works best for you in time. That said, I will share some things, and I am sure others will have more pointers and even conflicting advice, but as I say, beyond the basics, you have to find what works best for you. [I am not sure if there isn't a section on TF devoted to this already.]
The plant should NOT be dry and NOT just watered! (My use of the term "soil"= planting media/mixture.) You don't want to work with a mucky wet nor very dry soil/plant. If you can, water the plant few hours or a day or so before working with it. For "wet/tray method plants, simply allow them to drain of excess water a bit, before working with them.
* Also try to prepare the pots you are planning on planting into ahead of time, so they are ready when you are. Make sure to mix up extra soil mixture, so you don't have to stop to do that right in the middle of things. (* See additional notes below.)
Like un-potting any plant, I may gently squeeze on the sides of a plastic pot to loosen the plant from the pot some. Otherwise I grab the pot in one hand and the plant carefully and gently grasped in the other (to avoid inadvertently bending leaves and stems the wrong way). I sometimes slip the plant main stem between my fingers with my hand facing the pot to support the soil while also supporting the plant between my fingers...(I should shoot a video of this as its hard to explain on the fly...) I then turn the plant/pot & all up-side-down (or close to it) and tap the top edge (only) of the pot on the edge of my potting bench or table edge... (Pot facing down, the tapping motion will allow the momentum of the soil/pot-contents to loosen and pop it out of the pot!) Avoid smacking the plant itself into the table when you do this!
This should loosen the plant/soil/roots from the pot, often as one large "ball". It will be heavy and you want to support it when it releases from the pot, so as not to stress the roots and main stem(s). Just getting it to pop out, when successful, will allow you to flip it back upright back into the pot for the time being. This will give you a moment to ready yourself for what you want to do next.
Sometimes the soil-ball breaks apart during this, and can make things difficult
if the roots are stuck with some of the soil inside the pot, with the plant and some soil loosened up. I then use an old butter-knife to gently run along the inner pot walls, to loosen the soil/roots that are stuck in the bottom. (Don't worry too much about every little bit, but try to separate any big sections from the pot. Then once again grab it all and attempt to tap and separate it from the pot.
Having the soil ball break up is not a problem, but take care when working with the roots. Some plants have very brittle roots, and you don't want to break any more of them than necessary.
Which brings me to a RULE! I don't have many rules as far as this goes, but indeed this is important!:
Potting/Re-potting a plant is VERY important work and can affect the life of your plant dramatically! As such, when doing this, TAKE YOUR TIME, BE CAREFUL, TAKE YOUR TIME, DO IT RIGHT, TAKE YOUR TIME,& BE CAREFUL!!! (Did I mention, take your time?)
And I do NOT mean drag your heels either! You do NOT want your plant and roots drying out while you do this, and you do not want to do this in the cooking hot sun if you can avoid it!
With most CP's especially, you don't want to be disturbing the plants roots any more than you need to! So you want to do this once, do it right, and take your time to do it correctly AND GENTLY! Re-doing it is hard on a plant, and it takes time for a plant to recover and regrow roots.
**If you are just planning on re-potting the plant into a larger pot, Now is when you would remove the plant/soil ball from the original pot and place it into the new pot with planting medium/soil already in it.
* I usually try to judge how much soil to put in the new/larger pot first, so that final "soil-level" of the plant will be slightly lower than the top of the pot, when I put the plant into the "hole".
To do this, I estimate the distance from the top of the soil-line to the bottom of the root/soil ball (usually slightly less than the distance from the top of the soil-line to the bottom of the original pot itself). I then prepare my new/larger pot so that I have mixture in the bottom (running up the sides slightly) and the "hole" is about as deep as estimated. (It takes time to get good at estimating.)
I then position the plant in the hole (support the soil ball and plant when doing this), and then add soil/planting medium around the plant/root ball, gently pressing the soil down as you add mixture. I try to not put too much pressure on the roots themselves, but press straight down around the original soil ball, but not so much into it. You want to press a bit to get excess air pockets out, but not actually press so hard as to compact the soil too much. Watering it will also allow the mixture to fill in, if loose enough to move on its own, but this is not always the case. The term I learned was to "firm" the soil around the plant.
DO water the plant after potting it up. I sometimes dust a little rootone around the root ball, especially if the roots are showing. I sometimes do break up the soil/root ball, to spread the roots out or to remove old planting medium and replace with new. If you have never potted up before, try simply re-potting as described first, until you feel confident to actually break up the soil when doing this. (If you are really afraid to do this, try buying a cheap house plant to experiment on!)
Plants are a lot more resilient than most people realize, but you must take care when doing things.
Some plants however have very brittle roots, and it is sometimes difficult to work with them without breaking roots. (Especially depending on what was used to plant them in!)
I find that lowering the plant, pot and all into a bin of water (low plastic bins work better than deep buckets) and allowing it to sit for a while will help loosen the plant mixture. I do still try to "break" the plant loose from the pot first if I can, and then soak it in water for a while. I then remove the plant from the pot and slowly and gently separate the "soil" from the roots. When separating LFS from roots, this takes time and good observation to do it well. Don't be watching TV while you attempt this!
I haven't had much problem with Nep. roots, and dusting with rootone is often all I need to do to get the plant off to a good start. Ceph. roots are sometimes a little more temperamental for some people, so taking your time is essential. I sometime swish the plant thru the water to loosen the planting medium, but whatever you do be gentle.
I often separate my plants for propagation at this time, if the plant is large enough. Remember to try to prepare your pots up ahead of time if you can, as you don't want your plants sitting around naked for very long if you can avoid it!
Sometimes I remove the plant from the pot so I can "work with it". After loosening the plant, I simply turn the pot/plant over slowly and "pour" the contents out, while gently supporting the whole thing, and set it on the bench/table/some newspapers...whatever. (Set the pot aside.)
I can then loosen the soil from the roots, or examine the plant and mixture... look for rot, bugs, little army men, add rootone, insecticide, fungicide, separate it, or whatever I want to add or do. I then follow thru and pot it up, and WATER it to settle the "soil", help remove air pockets, and give the plant a good drink!
Well, its about 2AM and I don't know if I even wrote this correctly! I re-read this but my mind went to bed about an hour ago, so it didn't help. (I hope I can correct any mistakes I made in writing all of this.) I am sure I am forgetting a lot, and also probably have suggested things others would never do!
Please remember that that lump on our shoulders is what was given to us to think for ourselves! If anything I have suggested doesn't seem reasonable, then don't do it! If something I suggested doesn't work, try something different! We each have slightly different environments and slightly different abilities and ways of doing things. Firming soil gently may mean one thing to me and another to someone else! Learn from experience! Accept the fact that you may kill some plants! But don't let them die in vain! Learn from your experiences! You alone are responsible for them, not me, not some book, and certainly not some idiot working at the local nursery or hardware store! (Now-a-days, most people are working there for the money and could care less about actually knowing anything! BUT when you find someone who actually does care and especially one who DOES know something of value, then appreciate their help and respect their opinion! But keep in mind even still, YOU alone are responsible for your plants! DON'T let them down, they depend on you for their very lives!)
Good luck all!
Paul
[Most of this I mentioned, I learned starting back when I was about our youngest members age, having the unique opportunity to hang out and eventually working at an old fashioned "seed and bulb" store down the block from my folks business. Back then a kid didn't have to feel he needed to be an expert to be one of the group (While still a kid, I met a lot of old time plants-men and nurserymen) and just having the "plant-bug" and interest made you one of them! It was a very cool and wonderful time, as they shared tips and information freely, and above all joked around
and had a good time with one another!]
(Sorry this is so long, I hope it helped someone or at least made for interesting reading!