The central atom or group of atoms will have a positive charge, and the ligands will bond by compensating that charge with their own negative charge or characteristics. As the central atom has a specific charge, it has a maximum potential number of ligands (as each must donate at least one electron into the charge compensation equation) that it can bond to. These ligands will also arrange themselves into a certain arrangement around the central atom. If a single ligand bonds to more than one of these bonding sites on the central atom, then it is said to be bidentate (three=tridentate, etc)
These are named and described as if the central atom is in the middle of a polyhedron, and the corners of that shape are the locations of the ligands. For example, a complex with four, regularly distributed ligands would be described as tetrahedral.
Aside from the regular polyhedra, there are special descriptions, such as pyramidal (four ligands equally distributed in a plane, and one ligand normal to this plane).
Ligands which only bond to the central metal atom/ion through one side are called monodentate ligands. Some ligand molecules are able to bind to the metal ion through multiple sites, due to having free lone pairs on more than one atom, these are called polydentate. EDTA is an example of a polydentate ligand - it is able to bond through 6 sites, completely surrounding the ion. Polydentate ligands tend to be very stable, as it is necessary to break all of their bonds to the central atom for them to be displaced.