Bonds 101

Hydrogen

A hydrogen bond is a partially electrostatic attraction between a hydrogen atom which is bound to a more electronegative atom or group (such as nitrogen, oxygen, or flourine) and another adjacent atom bearing a lone pair of electrons. In other words, you have a hydrogen bound to something, and that complex is bound via the hydrogen to another something. The hydrogen containing thing is the bond donor and the thing with a lone pair is the bond acceptor.

Hydrogen bonds can be intra or intermolecular. These bonds are slightly stronger than a van der Waals interaction, and weaker than fully covalent or ionic bonds. They are seen in both inorganic and organic molecules. Consequences of hydrogen bonding include the high boiling point of water and the secondary and tertiary structures of proteins and nucleic acids. They vary in strength from weak to strong. 

Liquid water is a roiling mess of hydrogen bonds. Each molecule of water can form up to 4 bonds, 2 due to its lone pairs and the other 2 from donating protons. When a solute with a lot of hydrogen bonds is dissolved in water, the water is competitive in inhibiting the formation of hydrogen bonds between molecules of the solute. Each bond in water lasts an average of about 10 picoseconds.

Hydrogen bonding is largely responsible for the double helix structure of DNA. 

Ionic

Ionic bonding is the transfer of electrons from a metal to a non-metal in order to obtain a full valence shell for both atoms. All ionic bonds are at least slightly covalent, because a complete transfer of an electron is not something that can happen; some degree of sharing is always present. Atoms which have large differences in their electronegativities are said to bond ionically. Ionic compounds conduct electricity when molten or in solution. They generally have a high melting point and are soluble in water. 

Covalent

Covalent bonding is the sharing of electron pairs between atoms. The term includes many kind of interaction including signa bonding, pi bonding, and metal to metal bonding. Covalence is greatest between atoms of similar electronegativities.