Elements to the right of the "zig-zag" line containing the metalloids are known as nonmetals.
In the far right column we have the noble gases. These elements have 8 valence electrons (elements in the same column will always have the same number of valence electrons), giving them a full valence shell, which is very stable. Because of this the noble gases are inert, meaning they do not readily react. When other elements form ions or molecules, it is so that they can have the same number of valence electrons as the noble gases, 8.
One column over from the noble gases, in the column beginning with fluorine, we have the halogens. The halogens are one electron short of a full valence shell. Another column to the left, these elements are two electrons short of a full shell, the next column 3 electrons short of a full shell. So when these elements form ions, they GAIN electrons to reach the more stable full shell of 8 valence electrons. So they form negative charged ions, anions rather than cations.
Another way for nonmetals to achieve a stable full valence shell is to share electrons with another atom, forming a molecule via covalent bonding. For example, chlorine has 7 valence electrons, and would be a lot more stable with 8. Two chlorine atoms can each share an electron, so that each chlorine has 8 valence electrons around it some of the time.
Some differences between metals and nonmetals are that:
- metals tend to be shiny, nonmetals usual appear dull
- metals have high melting points, nonmetals have low melting points
- metals conduct electricity well, nonmetals are poor conductors
- metals have low heat capacities, nonmetals have higher heat capacities (so metals heat up more easily)
- metals are more dense than nonmetals
- metals are malleable and ductile (bendable and able to be drawn into thin wires), whereas nonmetals are not, they are usually more brittle.
Why is this? Well in a metallic solid atoms are close together and electrons are free to flow from orbiting one nucleus to the next. In a molecular compound, the attractive forces between individual molecules do not keep them as close together as in a metallic solid. (This is kind of a simplified answer, let me know if you want to know more.) One thing I haven't mentioned is properties of metalloids. Those elements can have some properties of metals and some properties of nonmetals.