One aspect of the Chinese menu that I should probably have explicitly covered somewhat earlier than this is the method of putting a meal together. Chinese dining differs from Western dining in that dishes are not served to individuals in strictly delimited courses, but to the entire table to share[see footnote 0]. This is the case whether the meal is a simple homecooked lunch or a grand formal banquet.
I'm going to discuss larger-scale restaurant-style meals today, since many of the principles hold for all types and scales of Chinese dining, and next week I'll offer some suggestions for eating Chinese food in smaller groups and at home.
One consequence of the "sharing" model is that the usual Western method of restaurant ordering, where each person decides individually what they want to eat with little or no reference to what everyone else wants to eat, doesn't always work too well. A meal should be balanced in terms of ingredients, flavours, and textures; and with the Chinese method of dining, if everyone's doing their own thing it's easy to end up with an imbalance. One way to overcome this is for the host (the person paying, or the person with the most experience with the cuisine, or the person who's been to this restaurant before, or the person who organised the outing, etc, etc) to decide what should be ordered, either unilaterally or in consultation with anyone else in the party who has an opinion.
Fuchsia Dunlop has an interesting blog post about the context in which a formal Chinese banquet is eaten. According to Gong Dan's Food & Drink in China,
a standard banquet will consist of four cold plates, eight main dishes, two major showpieces (such as a whole fish, suckling pig, or chicken), as well as soup, rice, pastries and fruit. I've not yet been lucky enough to participate in a meal this elaborate, though I have enjoyed a few Chinese meals in large groups, perhaps most notably a Hunan feast at Golden Day in London, where ten of us shared fourteen dishes including a whole steamed fish laden with chillies and garlic (photo of the fish).
It's worth noting that as sung points out in comments, the food at a formal wedding or New Year banquet is served in the style of a tasting menu, with one dish arriving at a time — I've previously linked to Red Cook's 2008 New Year banquet, which illustrates this nicely. This differs from less-formal restaurant meals, in which dishes may arrive in any order and all sit on the table together. With this difference noted, I'm going to take Gong Dan's list above as a framework for describing the type of dishes that I might order to make up a less-structured restaurant meal.
Working through the list in order, I've discussed cold dishes (涼菜/liáng cài) before. As I mention in that post, these are often labelled in English as "starters", but in reality they can be eaten at any time during a meal[see footnote 1]. At a restaurant, they will often appear on the table first (if only because many of them can be prepared in advance and just need to be dished out), but you're not expected to finish eating them before your hot dishes (Gong Dan's "main dishes") arrive.
Regarding the hot dishes, it's worth noting that these should not all be meat-based. Well-prepared vegetable dishes are just as "main" a dish as any meat dish, and in my opinion any Chinese meal is incomplete without them. In fact, the last time I was out for a Chinese dinner with friends, at least two of us felt that the Chinese leaf in spicy vinegar sauce (photo) was our favourite dish of the evening. If I'm out with a group, I like to order a dish of fairly plainly-cooked greens as well as the more strongly-flavoured vegetable dishes such as fish-fragrant aubergine or dry-fried green beans with minced pork.
Aside from the number of dishes served, the major difference between a simple meal and a more fancy one is perhaps the centrepiece/showpiece dishes. These can be thought of as analagous to, for example, the meat component of a Western "Sunday dinner", and they may in fact consist of roasted meat; a ham or a chicken, perhaps. (Personally, I prefer the "whole fish" option, but then I've never been a great fan of Sunday dinner!)
I've previously discussed the issue of soup (湯/tāng), and come to the conclusion that there's great variation in the way soups are included in Chinese meals. They may be served first, last, or throughout the meal.
Finally, an ample quantity of rice is a must. I usually serve/order plain rice with a Chinese meal, rather than fried rice. The reason for this is that many Chinese dishes are designed to be eaten in relatively small quantities with plenty of plain rice, and hence have strong flavours that can get overwhelming without the rice to balance things up.
Footnote:  Individually-plated courses are actually a relatively new development in British dining. Known as "service à la Russe", according to Wikipedia it dates back no earlier than the 19th century.
Footnote:  There's a discussion relating to the use of the term "starters" on English-language Chinese menus in the comments section of a recent post on sung's blog.