Oxidation and reduction can be defined on following bases.
Association or decomposition of oxygen: 

When oxygen is added to a substance, the substance is said to
be oxidized. When oxygen is removed from a substance, the substance is said to be reduced. In other words, addition of oxygen is called oxidation and removal of oxygen is called reduction.

Example: 2Mg + O₂ → 2MgO

Association or decomposition of hydrogen: When  hydrogen is added to a substance, the substance is said to be reduced. When hydrogen is removed from a substance, the substance is said to be oxidized. In other words, addition of hydrogen is called reduction and removal of hydrogen is called oxidation.

Example: 2H₂S + O₂ → 2H₂O + 2S

Association or decomposition of electropositive elements: Removal of electropositive element from a substance is called oxidation. Addition of electropositive element to a substance is called reduction.

Example: 2Kl + Cl₂ → 2KCl + l₂

Association or decomposition of electronegative elements: Addition of electronegative element to a substance is called oxidation. Removal of electronegative element from a substance is called reduction.

Example: 2FeCl₃ + H₂ → 2FeCl₂ + 2HCl

Exchange of electrons: When an element loses electrons, it results in oxidation of that element. When an element gains electrons, its results in reduction of that element. 

Example: Na → Na⁺ + e^–, 2Cl^– → Cl₂ + 2e^–