Sub Panel grounding questions... wire size, how-to's
Conduit is your friend here

As a general rule, using direct bury cable for an outdoor feeder is penny-wise and pound-foolish due to the cost of digging it up and replacing it when an upgrade is desired (a trencher rental + labor) compared to the cost of installing conduit (Schedule 80 PVC, or sometimes rigid metal conduit even) to begin with.  A 2" Schedule 80 PVC conduit between the buildings provides sufficient space at 742mm2 for 3 4/0 Al XHHW-2 conductors (at about 525mm2 total) and a 6AWG bare copper ground (which adds another 13mm2, to make for a total of 538mm2), while if you really want to go for broke, you could use 3" for easy pulling and extra expansion room (not that you'd need more than about 100-125A to an outbuilding, that is).

If you can't afford to do anything but stick with the cable...

If your only option is sticking with the cable you have, though, then what you can do is wrap a ground wire in with the cable as you lay it, as the NEC 300.3(B) requirements allow multiple individual conductors or cables in the same trench to be used as part of the same circuit:


  (B) Conductors of the Same Circuit. All conductors of the
  same circuit and, where used, the grounded conductor and all
  equipment grounding conductors and bonding conductors
  shall be contained within the same raceway, auxiliary gutter,
  cable tray, cablebus assembly, trench, cable, or cord, unless
  otherwise permitted in accordance with 300.3(B)(1)through
  (B)(4).


In particular, you'll need a 6 AWG bare copper ground wire for this, instead of the 8 AWG normally called for by a 100A circuit, due to the 250.122(B) size increase (which works out to a a size increase of about 1.6x over the base size from the table):


  (B) Increased in Size. Where ungrounded conductors are
  increased in size from the minimum size that has sufficient
  ampacity for the intended installation, wire-type equipment
  grounding conductors, where installed, shall be increased in
  size proportionately, according to the circular mil area of the
  ungrounded conductors.


You will need separate ground and neutral bars in the subpanel, no matter what

As a result of running a separate ground wire back to the main panel, you will need to have separate ground and neutral bars in the subpanel, with all the ground wires landing on the ground bars and all the neutral wires landing on the neutral bars.  Note that unless your panel shipped with extra ground bars factory installed, you will need to go to a local electrical supply house and buy a set that is appropriate for the make of your panel, or order the correct manufacturer's part online.

Furthermore, you will need to pull the (green) bonding screw or strap out of the subpanel and toss it, as it will not be needed -- neutral only meets ground at the main panel, as long as a separately derived systems is not sticking its nose into the tent, which only happens if you have a distribution transformer somewhere downstream of the main panel, or with certain generator configurations.

And you will also need that ground stake at the shed, as well

You will need some more of that 6AWG bare copper to connect the ground stakes (two of them, 8' deep and 8' apart) at the shed to the ground bar at the shed panel.  This provides a path for stray natural electricity to get back to the earth, while the ground wire between the main panel and the subpanel provides a path for wayward utility electricity to get back to the utility.