Atoms are the basic building blocks of matter. An atom has a dense nucleus composed of positively charged protons and neutrons which bear no charge. Protons and neutrons have approximately equal mass and contribute more than 99% of an atom's mass. The nucleus is surrounded by a circling electrons which have almost no mass and carry a negative charge. Despite contributing very little weight to the atom, electrons make up most of the volume. Once you get smaller than an atom, or start looking at the components of an atom, everything is the same. That is to say, a proton is a proton whether it's in the nucleus of an oxygen atom or a chlorine atom, but whole oxygen and chlorine atoms are distinguishable.
A neutral atom has an even number of protons in the nucleus and circling electrons; each proton has a +1 charge and each electron has a -1 charge so they cancel each other out. An element is defined by the number of protons in the atomic nucleus. Different versions of the same element called isotopes contain different numbers of neutrons. Different isotopes can have very different properties like radioactivity, but in general chemists are concerned with the electrons, which are determined by the number of protons in the nucleus of the neutral atom. In most cases, adding or subtracting a proton from the nucleus will have a greater effect on the reactivity and behavior of an atom than adding or subtracting a neutron.
Molecules are combinations of two or more atoms. Some elements do not occur by themselves in nature and are always bonded to another atom of the same element. These are called diatomic elements. Oxygen is one example, and the terms elemental oxygen and molecular oxygen may be used to distinguish between the lone oxygen atom and the molecule O2. Compounds are molecules made up of more than one element. So molecular oxygen would not be a compound; it only contains one element. All compounds are molecules but not all molecules are compounds.
Valency refers to the number of electrons which are available for bonding and tell you how many bonds an element can form. These electrons are located the furthest from the nucleus in what is called the "valence shell." Covalent bonds are formed by the sharing of electrons in a region of space between the nuclei of two atoms. Usually one electron comes from each atom sharing the bond. Carbon is tetravalent, meaning it has a valency of four, meaning that it has four valence electrons which are available for bonding. Carbon can form four covalent bonds, each bond containing one electron from carbon and one from the other atom. There are other, more complex factors that determines the type and number of bonds an atom can form, but valency is perhaps the most important factor determining an element's reactivity. Elements in the same column on the periodic table have the same number of valence electrons (they are equivalent) and as a result often have similar reactivity.