The wiring needs to be UF (under ground rated) wire if you do not plan on running it in conduit from the house to the shed.
It must be at least 18" under ground.
Never buy to small a conduit or it will be a bear to pull the wires.
Make sure to run a bigger sized wire then you think you may need. If you go undersized to try and save money and later on what to add an A/C unit, power saws, eletric heater, welder you would have to run all new wiring to do it.
The wiring is almost never run through the concrete floor at all unless the conduite was placed before the pore. It's almost always run over to the building through an elbow under ground and into a piece of conduit that stops just below the new breaker box, then into what's called an LB, then though the wall. (an LB amounts to an elbow but has a removable cover on it for pulling the wire.)
If the shed has vinyl siding on it then you need a siding block installed first to run the next piece of conduit through so the siding can move.
If it's a block building then you have to use a hammer drill to make a hole in the wall.
There's suppost to be conduit run all the way to the bottom of the breaker box to where it goes under ground. Your also going to have to run a bare ground wire and install a ground rod outside.
If your not sure how to do any of this then hire someone.