If it's without a change in trade, it's fairly easy...contact the gaining unit, make sure they have a position for you, find out if they're willing to transfer kit (this may have changed with the on-line clothing docs).
If it involves a VOT then it's a bit more complicated, involves a BPSO interview (which you should get done BEFORE leaving the losing unit so you don't end up NES at your new home).
I've bounced between 4 different Res units (11 Med, 6 FES, 8 FER, and 12 Fd Amb), and it's always been fairly painless, but I've always stayed in the same trade. Some units wanted kit back, others just transferred loan cards for unit-level issue.
DF