If I understand correctly... you can do the following:
GROUPING THE OBJECTS
Select all the objects used to make your card design -- images and text. Additionally, select the square surrounding them (representing the edges of your business card). This will make aligning the art to your other squares easier. With your images, text and the square selected, do one of the following:
1. right-click and select "Group" from the menu that appears.
2. click the Ctrl button and the G button
3. click Object/Group from the header menu.
APPLYING IT TO YOUR OTHER SQUARES
Now that you have all your art grouped, copy it and paste a duplicate onto your artboard. Select the pasted duplicate object and the pre-existing square you want to align it to. While both items are selected, click the square you want to align it to again -- the object selection edges should get thicker. Doing this tells Illustrator that you want to align the selected items to that object. Using your align palette (in the header menu, Windows/Align), align the edges of your duplicate copy to the top and left of the square you have on the grid. Continue this until all are done.
Depending on how you are printing, be sure to delete any extra "squares" (i.e., the boxes you made to show the edges of the business card), as you will now have twice the number (one from the pasted duplicate and one that you aligned to).