Are you in a campground or in a house?
If in a campground, I'd suggest talking to the management. I rather doubt they'd like you burying wires across your campsite. You may have to just run a heavy duty extension cord from the 120V 20A outlet on the pedestal to your shed, which is not a permanent solution but sort of acceptable in that a campground is not supposed to be a permanent residence (per the electric code people).
If it's at your own house, to do it properly will involve adding a circuit to your house breaker panel and running a wire to the shed. You should hire an electrician for this. There are indeed direct burial cables available, yes, but there are also varying requirements for how they can be used, and a host of other code details that an electrician would know about and understand how to follow. You can save some money by doing some of the labor yourself: in particular, digging the trench for the wire and refilling it afterwards would be a decent portion of the labor involved and doesn't require any very specialized skills.