Illustrator and Photoshop are powerful programs by themselves, but most artists find that using a combination of the two programs that enable them to produce beautiful artwork for publication. There are three basic ways to move Photoshop files into an Illustrator document.
You can "place" a Photoshop image into an Illustrator document, or place Illustrator artwork into a Photoshop file a using the File> Place command in either program. This is the "time-honored" method of moving a file into the other program. The only caveat is that the image (or artwork) must be in a file format that the other program can read.
Photoshop is very good at reading multiple file formats. Illustrator is a bit more limited in the formats it understands, but once a Photoshop file is in a readable format (eg TIFF, GIF, JPEG, etc.) you can simply use the File> Place command and select the image. Illustrator will place the desired image inside of the Illustrator file, and you will have some ability to manipulate the file within Illustrator.
The second way to introduce a Photoshop file into Illustrator (or vice versa) is the tried-and-true Clipboard. Simply copy the file elements you want from one program using the Copy command, and paste it into the other program using the Paste command. There are limitations to using the Copy-Paste method. It does not work so well for large files, and you can easily swamp the receiving program by pasting a large file into it.
The third method for introducing a file from one program into the other is dragging and dropping. If you want to take Photoshop art and put it in your Illustrator file, both programs must be open. Select the artwork you want to transfer, and simply drag it out of the Photoshop window onto the Illustrator window. To take Illustrator art into Photoshop, simply select the artwork from an open Illustrator window, drag it to an open Photoshop window and drop it into Photoshop.
You can also place paths from Photoshop into Illustrator files. Using the Path Selection tool in Photoshop, select and copy the paths you want to move, then paste them into Illustrator.