A while back someone mentioned "The Eater's Guide to Chinese Characters" by the late James D. McCawley. (In searching for the book I came across the University of Chicago's memorial page for him, and I've linked to it below.) They mentioned that the LA Public Library had two copies, a circulating copy at the Chinatown branch and a reference copy at the main library downtown. Well, I was downtown making a bus connection this afternoon so I stopped by the main library to have a look at the "Eater's Guide". What a blast! After about ten minutes of studying it, I was reading real Chinese restaurant menus.
Here's how it works. McCawley came up with a simplified system for classifying Chinese characters. For example, many characters consist of two distinct elements stuck side-by-side. Count the number of strokes in the left-side element (using a simplified stroke-counting system that, unlike most Chinese dictionaries, doesn't require you to know the conventional order in which the strokes are written), then refer to the directory of left-side elements (called L) in the back half of the book. In the outer margin of each page you'll find a complete list of the elements that comprise that many strokes, with brackets to indicate which of those elements are covered on the page you're looking at. Flip forward or backward until you find the page for your left element. Now look at the right element of the character, count the strokes, and look at the left-right combinations (which are ordered by the number of right-strokes) until you find the character. You'll get a translation for it, along with frequent ways that the character is combined with others to name specific dishes.
This sounds complicated, but I got used to it very fast. McCawley also explains (in the first half of the book) which characters you need to memorize and why, along with instructions for reading particular kinds of menus, writing down your order in Chinese for the waiter, interpreting the names of restaurants, and things like that.
If you want to find "The Eater's Guide", the main library is at Fifth and Grand downtown. Many buses go past it, including the 720 Westbound which runs along Fifth and stops right across the street from the library. You want to be on the lower level (new section of the library) that's devoted to science and technology; I think it's LL2. The call number is 641.03 M123. It's a reference book, but I found it shelved with the regular books (toward the back right corner of the room as you walk in the door) rather than with the reference books (directly to your right as you walk in the door). There's an information desk right inside the door with someone whose job is to help you find the book if you can't find it easily yourself. They have photocopiers, which I believe are on the far left side of the room, if you want to copy parts of it. Even copying the first several pages of the text (it's a small-format book) will get you a long way.