What methods are used to visualize a 4-dimensional Array?
I can't draw it here, but visualize it as a line (or array) of cubes.
Another way is to first take your cube representation for a three-dimensional array. Now replace the cube in your mind with a child's wooden block, and line up several of the blocks next to each other.
That's how I would teach it: a row of cubes. The position (or cube number) on this row is the 4th dimension.
And if you want 5-dimensions, now picture columns and rows - of cubes!
For 6 dimensions, picture the rows and columns of cubes (as for 5 dimensions), and now add "layers" of these rows and columns.
...For 7 dimensions, imagine all of the above - contained in cubes in a single row! ;)
Yup, it's cubes all the way down.
If you're trying to display output of a program for end users, then you are on the right track.
If you're trying to teach it, I'd briefly use that method, and then I'd go into depth explaining how the computer keeps them all in contiguous memory -- http://www.plantation-productions.com/Webster/www.artofasm.com/Windows/HTML/Arraysa2.html. I think this is the best way to understand it.
The original link is no longer working, but I found it up on the Internet Archive here -- http://web.archive.org/web/20120410120743/http://webster.cs.ucr.edu/AoA/Windows/HTML/Arraysa2.html
Updated first paragraph to show updated link, thanks to @OskensoKashi.