Before an actual landing most everything is speculation.
General speculations seems to float between two extremes.
- Leave the stage standing as it on the barge. Let it cool down, send in small crew in a boat, tie down the stage so it won't slide. Safe it and sail back to port in that orientation.
- After landing, approach the stage in a boat with a crane, lift the stage, retract the legs (unclear how, must be possible though) and lay it down in a cradle on the crane boat (faster transit back to port) or else on a cradle moved onto the barge.
The actual stage seems unlikely to tip over. It is a 140+ feet tall, but it is almost all empty tank, except for the engines and legs at the bottom. Center of gravity is very low, and the legs extend out 60 feet, so it should be fairly stable from tipping. Sliding is a bigger concern, since whatever the barges surface is made of, it is likely very durable since a rocket is landing under power on top of it. Throttled down Merlin, say 70% of 165Kbs thrust is on the order of 115 KLbs thrust. That will melt many things that be considered non-slip. Thus securing it in wave action will be critical, whether that is standing up, or on its side.
After the first two landings, the evidence seems to be two steps taken. Once landed, the crew comes in via boat. They use airplane jacks, and mount then under the engines, and lift the stage on them. They weld the jacks to deck to secure them, wherever the stage lands.
Then they weld caps over the tips of the legs as well to hold it in place.