The Scientific Method often consists of the following steps: (Don't worry if you don't understand it immediately. You should understand it once you do a few experiments.)

1. Observe and ponder: Observe the various phenomenon occuring around you - natural or artificial. Wonder why and how they occur.
2. Hypothesize and predict: Form a hypothesis (assumption) as to how, you think, things work. This hypothesis should be such that it can be proven to be false. Predict what you think you will observe. (Falsifiability is essential because you can't observe everything.)
3. Experiment: Now perform the experiment. There are certain precautions to be taken while performing the experiment. We will discuss these precautions at appropriate times.
4. Observe and take readings: Don't trust your memory. Write (or Type) down whatever you observe.
5. Conclude: Compare your predictions with your observations. If they match, what you have is a "theory". If they don't, then your hypothesis is falsified. You will need to form and test some other hypothesis.
6. Share your findings with others. Note that the scientific method is a cycle. Now, somebody else may perform the experiment to check if they get the same results you got. Or they may study other aspects of the phenomenon you were studying. Thus, the scientific method is a sort of a cycle.

Now, let's study gravity - it is the thing that pulls objects towards the earth. Read the following while referring to the corresponding points above.

1. We observe that objects thrown upwards come down. You drop a coin, it falls down. You drop a ball, it falls down. You drop a sheet of paper - hmm, it does come down, but it comes down slower than the ball or the coin. Why??? Could there be a relation between how massive (*heavy) an object is and how fast it falls down?
2. We hypothesize that heavy objects fall faster than light objects. So, one of our predictions is: even if two objects are similar, if I drop a rubber ball (or a coin, not a plastic ball**) and a football/basketball from a height, the latter will reach the ground earlier. Write down your hypothesis and the prediction(s). The general prediction is "heavier objects will always reach the ground earlier than lighter objects".
3. Now perform the experiment. Drop something non-breakable (rubber ball and basketball, or cricket ball, coin, a stone) from a height of 2-3 floors. The height should be such that you (or your friend) should be able to distinguish which object touched the ground earlier. Take care that no one is standing below the object, else s/he may get hurt.
4. Note down your observations.
5. Now conclude. What you would observe is that, some times, both the objects may reach the ground at the same time. Thus, heavy objects do not always reach the ground earlier than light objects. This means our hypothesis has been proven false. In science, there is no such thing as being proven right. The hypothesis can only be proven wrong. This occurs when the observations do not match the predictions. Of course, care must be taken to ensure that the observations are taken properly.
6. You may want to share this finding of yours with others. Well, until about 400 years ago, [most] people believed that the heavy objects fall faster than light objects. It was Galileo who performed a similar experiment (alternate link) and proved that this belief is incorrect. And now, most of the educated people know that both a heavy object need not reach the ground faster that a light object. So, don't get disheartened if other people may not be impressed with this finding!

This is a really simple example. There are techniques for dealing with hypothesis which say something like "A occurs 75% of the time" instead of just saying "A occurs always".