Just remember this is all just physical, so the best way is to scribble a layout on the paper (both sides) the way you want it folded, then spread it out unfolded.
Then reproduce that in the same page size layout in Pages.
If you need to, copy the material on the layout to get the double layout.
To get everything to print in the right position on the paper, experiment with which way you have to feed it in again (to get the other side) into the printer.
Probably (without seeing your actual booklet) this is what it will look like with page numbers. Page 1 is the front, 4 is the back and 2,3 are the inside:
First page in Pages:
4 | 1
4 | 1
Second page in Pages:
2 | 3
2 | 3
Print the first page from Pages, feed it in turned over in your printer. This may actually be face up to you, many printers turn over the sheet as it goes through.
Then print the second page from Pages.
Then cut the double sided print in half and fold it.
If I'm reading your description correctly, you want to produce a four page booklet (cover, inside left, inside right, back), with two copies, arranged one above the other, on a US Letter (or A4—the paper sizes differ, but the process is the same) sheet.
There are several ways to do this. The simplest, perhaps—provided your printer supports printing four pages on a single sheet, is to create the document with eight full size pages, then print four-to-a-page onto two pages (or onto two sides of a single page, take the result to a copy shop and print as many copies as you'll need, cut them into two and fold the half sheets to produce the booklets.
If your printer supports multiple pages on a single sheet, it will likely also offer choices of how to proceed through the document pages when printing. For the choice below, you'll need to set up the eight pages in the order listed below the image:
P1, P3: BC
P2, P4: FC
P5, P7: Inside Left
P6, P8: Inside Right
Print the first four pages to one sheet, the second set of four to another sheet, then at the copy shop, do a test copy of the two sheets to 2 sides of a single sheet. when you've established how to feed the originals into the copier to get the desired layout, finish your full run, cut and fold, and you're done.
Note: You will probably need to reduce the margin allowance from the default 1 inch all around. This is done using the (Document) Inspector.