The atomic number is the number of protons in an atom, and the number of electrons in an atom equals the number of protons in a neutrally charged atom. (Negatively charged atoms, or negative ions, have more electrons than protons, and positive ions have fewer electrons than protons.) Finding the number of neutrons requires a bit of math.
Search for an element or atom on the periodic table. Note the atomic number, a whole number, usually found in the upper-left corner of the element box and the atomic mass, in decimal notation, usually located on the bottom of the element box. These are the only values you'll need to find the average number of neutrons in the atom.
Round the atomic mass of the atom to its nearest whole number. For example, Calcium's atomic mass is 40.078, so it rounds down to 40. Nickel's atomic mass is 58.6934, so it rounds up to 59.
Subtract the atomic number from the rounded atomic mass. The difference is the average number of neutrons in the atom. For Calcium, subtract 20 from 40 and obtain a difference of 20. Subtract 28 from 59 to find that Nickel has 31 neutrons.