First, run these tests. At 15-20 mph. remove your hands from the wheel on a flat, straight surface. If the wheel swings slowly and gently back and forth, you have low tire pressure--low enough and it could seem far worse at higher speed.
"Shaking" isn't descriptive enough. Now, at 45 mph or so, depress the brakes steadily and gently. If the wheel swings back and forth you have warped rotors (or discs), and I'll bet the pads are worn unevenly, too. This can happen on a low mileage car if the wheel nuts were tightened beyond specs and the car was left standing for a while. If you brake at high speed and the whole front shudders without any side-to-side swing, it's either discs, a blown bearing or a loose front end part like a tie rod end. If the front end clicks during turns, it's a shot CV joint.