What the Megaminx is
The Megaminx is a dodecahedron: twelve five-sided faces, each turning in fifths of a rotation. Solving it uses the same ideas as a 3×3, but there are far more pieces, and there is no practical way to generate a scramble from a random position.
Reading R++ and D--
Megaminx scrambles don't name individual faces. R++ turns the whole puzzle except the left face by two-fifths of a turn; D++ does the same around the vertical axis, everything except the top face. The doubled sign shows the direction: ++ is clockwise and -- is counter-clockwise, as seen from the right for R and from below for D.
Each row ends with U or U', a single fifth-turn of the top face. Apply the rows one at a time from left to right.
How the scramble is generated
The scramble is a random sequence in this R/D format, the same scrambling style the WCA uses for the Megaminx: 70 big R and D turns plus 7 top-face turns, enough to mix every piece.
Practising the Megaminx
A full Megaminx scramble takes a while to apply, so do it carefully once rather than quickly twice. At WCA competitions the Megaminx is an average of five; practise the same way and keep an eye on the average, not the occasional fast solve.