steps 1: downdload both required file, cyanogenmod 13 android 6.9,1 marshmallow rom and marshmallow gapps and move them to the internal storage of your glaxsi s3
Steps 2: turn off your galaxsi s3 and boot into recovery mode,TWRP or ghilz.to do so press and hold the volium up, hom and power key,s and the same time
Steps 3: once in recovery ,make the full nnardriod backaup..the rom is not suterbal.and will go back to your previous rom.
Steps 4: wipe data,chach and dalwik chache.
Steps 5: flash CM13ROM and then flash marshmallow gapps
reboot youer pohn and get redy enjoy your new marshmallow divice