Well the straightforward answer to this is that you cannot really “crop” a photo in Illustrator because there is no “crop tool”. Illustrator serves a different purpose as a designing package.
However you can use what is called “Clipping Mask” within Illustrator to achieve similar result.
Lets see how it is done
First open a photo in Illustrator as shown below
As you can see that the photo bounds overflows the art board. I would like only my face to be included in the photo and would like to remove the rest.
What I did next is I moved my picture a little bit down and then drew a rectangle of the size of my art board as shown below
Now select both object i.e. rectangle as well as the photo. Now goto Object > Clipping Mask -> Make as shown below
End result will look something like this
I hope this helps. On a Side note I would recommend using photoshop or even MS Paint to crop your Image. The problem with Masking is that the photo Dimensions remains the same after doing the above. Because what essentially masking does is it fills up the masked bounds with white transparent space.
PN: My level of using Photoshop and Illustrator is beginner to intermediate.