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Opening Illustrator Files in Photoshop
In Photoshop, simply go to File> Open and navigate to your Illustrator document. Photoshop will choose the format for you, in this case calling it "Photoshop PDF".

Next, enter the image size. This can be as small or as large as your project requires. Of course, if you choose an enormous file size and/or resolution, it may take a while to open. Check Constrain Proportions, otherwise the image's aspect ratio will be distorted.

If the preview doesn't look right, it's likely that the illustration is falling outside the Illustrator artboard. In this case, you'll have to go back to Illustrator and adjust the image or the artboard dimensions.

The new Photoshop file will have a transparent background and be on a transparent (i.e., non-Background) layer. From here you can use the image in a composite, use it as a mask, apply Photoshop filters to it, etc.

Exporting an Illustrator file to Photoshop
It's easy to export an Illustrator file (EPS or native AI) to Photoshop. This will give you more flexibility than simply importing it in Photoshop. If the Illustrator file is built with layers, those can be preserved in the export, as can any live type. In this example, each county of the map is on its own layer. In addition, there are separate layers for the state outline and the text.

In Illustrator, choose File>Export. Select Photoshop (psd) as the format.

the resolution, then select Write Layers and Maximum Editability. Note that these options are only available when you choose CMYK or Grayscale color modes, not RGB.

Now when you open the newly-exported file in Photoshop, you'll see the same named layers that were in the Illustrator file, including any sub-layers.

From here, you can select the layers individually and apply filters and effects, show/hide each layer, or rearrange them to your liking.

You can also edit the type. Each type object gets exported as its own layer in a layer group, and can be modified with Photoshop's Type tool.


Conclusion
Follow these simple tips, and in no time, you'll be in the import/export business!