Wheel lug studs sometimes become damaged or broken and must be replaced. Doing it yourself requires no special tools.
If a wheel has loosened and worked back and forth on the studs, replace all of them. Studs are inexpensive and there's no use taking chances.
With the wheels chocked, loosen the lug nuts about a quarter turn. Jack the car up and place a jack stand under the axle housing (rear wheel) or lower control arm (front wheel) of the wheel you're going to remove. Let the car down so the jack stand is supporting the car, but the wheel is still an inch or so off the ground. Remove the lug nuts and lift the wheel off. If the stud you're going to remove is on a disk brake, with a heavy hammer strike the end it.
If after several tries it hasn't started to slide out, spray the stud liberally with penetrating oil, let it soak in then attack it again. (Try not to get any oil on the brake rotor or the surface of the rotor where the brake pads touch it. If you, do, spray with a brake cleaner.) Once you have the stud out, take it over to an auto parts supply store and get a matching size.
When you insert the new stud, make sure the splines line up. Then push the stud in with your fingers as far as you can - which won't be very far. Spray penetrating oil on the splines, then whack it with your hammer until you get it in.
You may find you can't drive it all the way in the with the hammer. No problem. As long as you've got it in far enough to screw a nut on it, you can use the nut to draw it the rest of the way.
With drum brake (on the rear wheels of most cars) the only difference is that, after you remove the wheel, you must remove the brake drum. Inspect each stud where it comes out of the brake drum. Some should have a retaining clip. Remove clips with pliers. Make sure the parking brake is off - otherwise it won't let you slide the brake drum off. If it seems stuck, try working it back and forth in a side-to-side motion to break it loose, or strike it smartly with a rubber mallet. Don't hit it with a metal hammer (you can damage the drum).