If you're not exercising regularly, the answer to how much protein you need is pretty simple: Government recommended levels are more than adequate - around 0.3-0.4 grams per pound of bodyweight. However, if you're lifting weights, running, cycling (or taking part in any kind of physical activity, for that matter) you should probably up your intake a little.
While exercising, you put more stress on the body. When you train, you damage muscle cells. Protein synthesis is the process whereby biological cells create new proteins which help repair and rebuild the tissue. Higher levels of protein help with this process as well as contributing to improved brain function and insulin response.
When endurance training, you should up your intake to around 0.45-0.65 grams per pound of body weight - depending on level of activity. If powerlifting, or looking to bulk up, this increases further to around 0.75-1 gram per pound. There are rarer situations where it is necessary to increase intake further. For example, if you are training 5 times per week, you are in a caloric deficit, you are already very lean, and you are looking to build or preserve muscle you should consume more than 1 gram per pound. Even so, the upper limit should be 1.4 grams per pound of body weight.
When planning your diet, it is important to take account of whether the protein is complete or not. Bread, for instance, contains protein but lacks certain amino acids. This means that it is "incomplete". However, by combining bread with other foods (such as beans, which contain the missing amino acids), you can form a complete protein. A complete protein is one which contains all nine essential amino acids.
When it comes to forming complete proteins, it can be hard work trying to find foods which complement each other. For this reason, there is a great site which allows you to examine the protein profile on thousands of foods. When viewing an item, there is even an option to view foods with complementary amino acids profiles.
Calculating Daily Requirements
If you are unsure about how much protein you need while exercising and/or dieting, there are a few online calculators which can help you find the answer. This is probably one of the better protein calculators as it takes account of a wide range of criteria while including references to the research used to build it.