Both hydrogen atoms need to gain one electron to have a full outer shell. Oxygen needs to gain two electrons to have a full outer shell. When the covalent bond is formed, hydrogen has a full outer shell because it oxygen shares one of its electrons with each of the hydrogen atoms. Oxygen has a full shell because each hydrogen shares its electron with oxygen.

Note:

1. It is conventional when drawing covalent bonding diagrams such as the one shown above to use some notation to distinguish between electrons from different atoms. The example above uses different colours but dots and crosses are also often used. (You may hear these diagrams being referred to as "Dot and Cross Diagrams".) It's important to remember that, in reality, there is no difference between the electrons.

2. The diagram above shows all the shells of oxygen, for the sake of completeness. In practice, it is only necessary to draw the outer shells, as these are the ones involved in bonding.