This kind of noise comes from the hydraulic valve lifters sticking. It usually is caused by not changing the oil and oil filter as often as recommended. It also will be made worse if you use different brands of oil at different times. Only one brand of 10W-30 oil should be used. This same brand and weight of oil should always be used whenever the oil is changed, and if any oil is needed between changes.
The hydraulic lifters have closely fitting parts in them. If you use a thick oil treatment (like STP or motor honey) it will clog up the small oil passages in the lifters and make the noises worse. There are 2 different types of oil additives on the market. One type makes the oil thicker, and the other type makes the oil thinner. The only additive that can help with a lifter noise problem is a thin penetrating additive, like Marvel Mystery Oil. Thick additives are made to reduce the rate at which a motor burns oil; but they also harm the engine by interfering with lubrication of closely fitting parts. Thick oil additives should never be used in an engine that is in good condition.
The proper way to repair this problem is to replace the hydraulic lifters, and inspect the condition of the pushrods and rocker arms. Any worn or damaged parts must be replaced; and the rocker arms should be adjusted to the manufacturer's recommended setting (usually 3/4 to 1 1/2 turns down from zero lash) while the motor is idling, at normal operating temperature. If you do this at home, buy a set of rocker arm oil stop clips and attach one to each rocker arm on the pushrod end. This will prevent oil from spraying all over the motor.
Sometimes an engine can be quieted down simply by readjusting the rocker arms to the above specification; but this will only help if the valve lifters and valve train are not damaged.
Sometimes noises like this can be caused by deposits building up on intake valve stems, which make the valves stick and prevent them from closing completely. This kind of situation can often be corrected by buying a large bottle of Chevron Techron fuel system and combustion chamber cleaner, and adding the contents of the whole bottle to the fuel tank just before filling the tank with fuel. It usually takes 50 to 75 miles of driving for this unique formula to clean deposits out of the engine.
If the engine is old and sludged up; there is one particular additive which can clean it out and free up sticking parts. Sometimes this will increase the rate of oil consumption; but it usually just makes it run better. This additive is called Kreen. It is made by Kano Labs in Tennesee. This is the best engine cleaning additive I've ever seen for this purpose. It can be ordered from http://www.kanolabs.com/engCle.html
You can use this according to the directions on the can; but I've had even better results by draining out enough engine oil so that it is one quart low; and then adding 1/2 quart of Kreen and 1/2 quart of Pennzoil ATF automatic transmission fluid to the engine. Drive the car for 1/2 to 3/4 hour like this, not going faster than 45 mph and not climbing steep hills. Then drain the oil while it is still hot, and change the oil and filter. Add Kreen to the new oil as recommended on the can for regular use.