There are three basic methods for moving a document between Photoshop and Illustrator.
Both programs respond to a File > Place command to either "place" Illustrator artwork into a Photoshop file or a Photoshop image into an Illustrator document. This is the most traditionally used method among users for moving a file from one program to the other.
The caution in this method is that the artwork or image must be in a file format readable by the other program.
Photoshop is very adaptable at reading various file formats. Illustrator has a few more restrictions in the formats it recognizes, but once a Photoshop file is in an understandable format (i.e. TIFF, GIF, JPEG, etc.) using the File > Place command with the desired image is simple. Illustrator will "place" this image inside the Illustrator file and allow you some manipulation of the file in Illustrator.
Another way of moving a Photoshop file into Illustrator (or vice versa) is with the Clipboard. Just copy the file essentials you want from one program with the Copy command and paste it into the other program with the Paste command.
There are limits to the Copy-Paste method however. This method does not work well for large files and you can easily overload the receiving program by pasting a large file into it.
The last method to consider in moving a file between these two programs is the Drag and Drop method. In order to do this, both programs must be open at the same time. Choose the artwork you want to transfer from Photoshop for example and simple drag it out of the Photoshop window onto the Illustrator window. To move artwork the other direction, simple choose the artwork form an open Illustrator window and drag and drop it into an open Photoshop window.