Chemical Bonding

There are three general types of bonding. Covalent, Polar-Covalent, and Ionic bonding.

Covalent bonding is when an atom shares its electron in the process to become stable. For example, a hydrogen would bond with another hydrogen, as it fills it's first orbital, and therefore becoming a stable element.

Polar-Covalent bonding is like covalent bonding, but it involves two (or more) different elements. To understand how this works, you'll need to understand valence electron orbitals.

Short version: If its in group 1A, it has 1 valence electron, 2A, two valence electrons, etc. Once it has eight valence electrons, it becomes stable. Transition metals (Group B elements), Hydrogen, and helium are an exception to this.
Take water as an example (H2O). Oxygen is in group 6A, and so it has six valence electrons, needing two more to complete its valence octet. Hydrogen has 1 valence electron (1A), so two Hydrogens share their electrons with Oxygen.

Why is it polar? Oxygen is more "Electronegative", or how much it wants the electrons. Oxygen is more electronegative, so the electrons want to be with oxygen more than Hydrogen. Oxygen's lone electron pairs that act as bonded electrons, pushing away the hydrogens, making the asymmetrical shape.

Ionic bonding is where an atom "donates" an electron to another atom. For example, Sodium Chloride (table salt). Sodium is in 1A, while Chloride is in 7A. Needless to say, one electron goes from Sodium to Chlorine, and they both become stable.