Been there and done that many of times with the regular garden and my favorite one
and the best way I have found is to clean a spot off the patio with the hose and then take said hose and while on a gentle shower setting spray all the dirt off and then gently separate the two ..or three plants roots with your fingers ( a kitchen sink with a sprayer will work but the dirt is an issue with the drains ya know so be sure to watch that if ya do it in the sink )
Kinda run your fingers down through the roots like ya would with a nice brunette ya know
If they are real tangled I have found that if ya do it in a 5 gal pail of water it makes it easier ( the root part not the dirt removal part !..that's just making mud then ya know ) .. oh and while I stress to do it gently if ya do tear a few of the roots all is not lost since plants are way tougher than most would think ... I usually count on at least a week being added to my finish times from doing it but do it I do do at times and always successfully
Be forewarned though .. ya need to have what ever medium you are transferring to and the pot right there and get er done without hesitation since while they are tougher than ya think they do get more stressed out the longer ya play with em
Peace .and good luck