All matter is made up of atoms in various arrangements. Atoms are composed of protons, neutrons, and electrons. Each proton has a charge of +1, each electron a charge of -1, and each neutron has no charge (neutral charge--neutron). Atoms of the same element all have the same number of protons, by definition, because elements are defined by how many protons they have. Having different numbers of neutrons in the nucleus will not affect the charge of the atom. Instead, different isotopes have different mass and have different tendencies to radioactively decay. Different isotopes behave basically the same way chemically, because chemistry is determined by the electric charge. There are some slight changes in the chemistry of different isotopes of hydrogen, these isotopes are called protonium (no neutrons, the most common form), deuterium (one neutron) and tritium (two neutrons).
An example to illustrate the point would be different isotopes of carbon. Common isotopes of carbon include carbon-12, carbon-13, and carbon-14, often written as 12C, 13C, and 14C. These types of atoms have 6, 7, and 8 neutrons respectively. 12C is the most common carbon isotope in nature. 14C is famously used in archaeological radioactive dating. (See hyperphysics for more on carbon dating).
In most types of nuclear power production, a specific isotope of uranium, 235U, is used. This is the only naturally occurring fissile nucleus found on Earth (although people have made other fissile isotopes of plutonium). In nature, uranium exists as a mixture of 238U, 235U, and 234U. 238U is by far the most prevalent. The uranium used for nuclear power in most nuclear reactors is processed to have a higher ratio of 235U to the other isotopes than normally occurs in nature. This process is called "enriching” uranium and is a very difficult engineering challenge.
The University of Colorado has graciously allowed us to use the following Phet simulation. This simulation explores how adding different numbers of protons and neutrons make different isotopes: