The valence (or outer-most) electrons are the easiest to lose. In covalent bonds, electrons will be shared between two atoms. In ionic bonds, the atom with less valence electrons has a tendency to give them up to the other atom.
Here's an example using water:
The oxygen has 6 valence of it's own, and each Hydrogen has one. A - is a bond of 2, while a = is a bond of 4, and an * is a single valence electron. The oxygen's goal is to have a complete valence shell, which is 8. While the Hydrogen wants one as well, which is 2 for Hydrogen.
This is what the structure would look like:
** H-O ** | H
Each Hydrogen has a single bond (2), and the oxygen also has those single bonds (2 single bonds is 4). Then the oxygen also has 4 valence electrons of its own still. 4+2+2=8 for the Oxygen.