Do they lay it out pretty much exactly like it appears in the stone?
Somewhat! The one exception is that "line wrapping" is sometimes redone: if the original text consists of multiple lines or columns, the breaks between those are removed, and new line/column breaks are added based on the size of the paper. Sort of like how zooming in or out on this answer might change the positions of line breaks in the text, but won't change the positions of letters within a word.
And do they have a system or are they laying it out like you layout on PowerPoint and just manually place each piece?
There's a standard called the Manuel de Codage, which specifies how different arrangements of glyphs should be turned into a linear stream of ASCII characters. Typesetting programs like LaTeX can then turn that into nicely-arranged symbols on a page.
My favorite system for this (though I haven't used it much) is Sesh Nesout, aka HieroTeX. But there are many others out there.
Is there a pattern to it or is it all over the place?
The glyphs are meant to be read in a linear order; this is a universal across writing systems for spoken languages, since they're representing a linear sequence of phonemes. The structure is sort of recursive: one book might contain several pages (read left to right), each made of lines (read top to bottom), each made of blocks (read left to right), each made of symbols (read top to bottom).
You'll notice English orthography does almost exactly the same thing, just one level less (we don't have vertical blocks within our horizontal lines).
Has anyone come up with a Unicode layout system for the Gardiner hieroglyphs?
Unicode doesn't do layout or formatting, as a general rule. And its support for hieroglyphs is mostly limited to "here are some codepoints for the signs in Gardiner's list". Any fancy arranging has to be done in an external system, like LaTeX.