The construction is exact and easy to state. Take the thirteen circle centres of the Fruit of Life. Connect every centre to every other centre with a straight line. Thirteen points taken two at a time gives seventy-eight lines, and that is the entire figure. No line is selected and none is omitted, which is what makes this a determinate construction rather than an artistic composition.
Two things are worth pinning down because they are frequently got wrong.
The first is the source. The figure is built from the Fruit of Life, the thirteen tangent circles, and not from the Flower of Life, the continuous nineteen-circle lattice. Drawings captioned as Metatron's Cube laid over a Flower of Life background are extremely common and are simply mislabelled: the underlying sets of centres are not the same, and the Flower's centres would give a different and denser figure.
The second is the count. Because the thirteen centres lie on a regular triangular lattice, many of the seventy-eight connecting lines are collinear with others and overlap visually, so a drawn version looks like far fewer than seventy-eight strokes. Seventy-eight is a combinatorial fact about the points, not a count of visibly distinct segments on the page.
Despite the name, the figure is two-dimensional throughout. Why it is called a cube is not documented in any early source; the usual explanation is that a cube viewed in isometric projection is among the shapes readable in it, which is at least consistent with how the figure is used.