Reading the Periodic Table
The Atomic Numbers are the consecutive whole numbers on the periodic table (1,2,3, etc). Each element has its own number. An element's atomic number equals its number of protons, since an element changes when you change the number of protons. Examples: 1 is the Atomic Number for Hydrogen and Hydrogen has 1 proton; 20 is the Atomic Number for Calcium and Calcium has 20 protons.
The Atomic Mass tells us how much mass an element has. (Not exactly how heavy it is, but that will do.) The atomic mass has units of amu (atomic mass units). You can always tell the atomic mass numbers because they are not consecutive or whole numbers. Why? Because the atomic mass does not count the number of masses (protons and neutrons), but how much mass it has. By adding up the number of electrons, protons, and neutrons you never get a whole number. This is also that in order to keep the protons and neutrons together (the protons are positive and trying to repel each other) part of their mass must be converted to energy in the form of the strong nuclear force to hold the atom together. (More info here.) Examples: Hydrogen's atomic mass is 1.008 amu; Potassium's atomic mass is 40.08 amu.
Chemical Symbols are used to make writing chemistry easier (instead of writing out long element names). Each element has only one capital letter. Two capital letters stand for two elements. Since there are several elements that start with the same first letter, make sure to check the periodic table for the chemical symbol. The symbol may not be as obvious as you'd think. Examples: C is Carbon; Ca is Calcium. Au is Gold, not "G".
Groups are the columns (up and down) of the periodic table. (More info on Groups here) Elements in the same group have the same number of valence electrons (outer electrons). (More info on valence electrons here) Examples: Hydrogen and Lithium are in group 1 and both have 1 valence electron. Boron and Aluminum are in Group 13 and both have 3 valence electrons.
Periods are the rows of the periodic table. (More info on Periods here) Elements in the same period have electrons in the same orbit. When the electron orbit is full, you need to move to the next orbit, and the next row (period) on the periodic table. Examples: Lithium (Li) and Beryllium (Be) are in period 2 and have electrons in the first two electron orbits. Oxygen (O) and Sulfur (S) are in different periods, but the same group.