Depends on the sim card size your current phone is using. If your phone currently has a micro sim, then you'll either have to cut it or activate the nano sim that comes with the GS6 (can easily be done online). If your current phone has a nano sim, then just pop it into the S6 and you'll be good to go.
I have a Note 4 which uses a micro sim card. I ordered an S6 which uses a nano sim card. I bought a sim card adapter so that I can put the nano back in the Note 4 if I need/want to.