Atoms are made up of electrons, protons, and neutrons. Neutrons have no charge. Forget about them.
Each proton has 1 unit of positive charge. Each electron has 1 unit of negative charge.
If the number of protons and electrons is equal, the atom is neutral (opposite charges cancel each other out).
If the atom gains or loses an electron, it will either become positively charged (if it loses an electron) or negatively charged (if it gains an electron). This can happen lots of ways. Different chemical processes result in electrons being gained or lost. You can even physically knock electrons out of atoms (rubbing your feet over a carpet to gain an electrical charge to shock someone, for example).
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