Protein shakes have done two things for me.
First, a morning protein shake -- which I have done now for about 5 years -- helped me take control of my diet. It allows me to make breakfast my biggest meal, giving me all day to burn the calories, instead of eating a big dinner and then storing it as fat while I sleep. Since I load it up with fruit, I also get my fiber. It is also super easy: throw everything in the blender and you are good to go.
Second, protein shakes helped me build muscle after lifting weights. I don't actually do that right now, since I've been working out mornings lately. But, when I worked out at night, it was standard to toss down a quick shake -- powder and almond milk -- before or after. I'm not a bulky guy -- alas, that is not how I am built -- but the protein definitely helps my body recover from a good workout.
The previous commenter is right that too much protein just gets dumped, but adding a 30-gram drink to your day doesn't even get you close to that, I wouldn't think.
He's also right that there are companies out there selling protein making all sorts of questionable claims. I just stick to Whey protein that mixes well and tastes good and is not too expensive. Currently, that is GNC because Rite Aide often has sales on it. The strawberry is the bomb.
Protein powder has helped me cut sugar and reduce my daily carb intake. Now, I could just eat a lot of meat or other sources, such as beans, but powder is much easier. And, it tastes great.
As to how much: 1 gram per pound of your targeted body weight (the weight you want to be. For me, that is always less than I actually am) is the general goal. It is less for women, maybe half to three-quarters of a gram? I don't count such things anymore -- maybe I should, just for a reality check? -- but I rarely got that much into me, even with two shakes a day. Basically, I throw in one scoop per shake these days and each scoop is around 30 grams.
I'm a 56-year-old guy and I lift three times a week and do cardio in between, when I'm being good. I'm just trying to stay strong so I can keep active.
Since I am gassing on here, I'll add that my shake typically includes powder, peanut butter, Greek yogurt, blueberries, some other fruit and almond milk (because I avoid dairy) My wife's shake has cranberry juice as it's base. My buddy Brant puts so many greens into his that it glows alarmingly.
Finally, Men's Health has a ton of good information online, if you want to research it.