I agree with the PP that when going to Studios it's probably just as easy to take the boat (dock is at Yacht Club) or walk.
For Animal Kingdom, exit the Beach Club onto Epcot Resorts Boulevard (it really doesn't matter if you go left or right because Epcot Resort Boulevard is a big U-shape - you'll ultimately end up at the same road). When you reach W. Buena Vista Drive, make a right (there will be a light). Stay on this for a while, until you start seeing signs for Animal Kingdom (you'll go past Coronado Springs and Blizzard Beach). Make a right onto Osceola Parkway (it's a ramp on the right). Stay to the right and follow the signs into Animal Kingdom's parking lot.
Within WDW, there are lots of signs that make it pretty easy to get from place-to-place (especially the theme parks).
I didn't drive there, but for the Studios I think the easiest option is to turn right as you exit the Beach Club parking lot. When you get to the intersection with Buena Vista Drive, go straight and that should take you directly into the parking lot for DHS.