The best way is simply to know how the various dishes on the menu are cooked (e.g. fried, sauteed, steamed, boiled). Items that are described as being fried, deep-fried, pan-fried, shallow-fried or sauteed are going to have a relatively high fat content simply due to the nature of these cooking methods.
Look for items on the menu that are described as being poached, steamed, boiled, grilled (taking grilling to mean over high heat with very little added fat, though this is not always the case), roasted or baked. These would generally be lower in fat than the ones I mentioned earlier. Stir-frying can be a bit hit and miss; although you can do it with fairly little oil, it is traditional in Chinese cooking (as far as I know), for example, to use substantial amounts of oil when cooking in a wok (of course it depends on the dish as well).
Additionally you also look at what the dish actually contains such as sauces or dressings (e.g. vinaigrette, mayonnaise, hollandaise, coconut cream or milk) and side dishes (e.g. mashed potato, polenta are typically made with fair amounts of butter/cream/cheese).