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How does beta decay change one element into another?

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A color-coded periodic table of the elements displays each element's symbol and atomic number, with categories such as alkali metals, noble gases, halogens, transition metals, and actinoid elements distinguished by different background colors. — actinoid element Modern version of the periodic table of the elements (printable).

Beta decay changes one element into another by altering the number of protons in an atomic nucleus, which defines the element's atomic number. This process is a form of transmutation, governed by the weak force.123

There are three primary ways this occurs:

Negative beta decay ( $β^{-}$ ): A neutron in the nucleus transforms into a proton, emitting an electron and an antineutrino. This increases the atomic number by one while the mass number remains the same.14
Positron emission ( $β^{+}$ ): A proton in the nucleus transforms into a neutron, emitting a positron and a neutrino. This decreases the atomic number by one.1
Electron capture: The nucleus captures an orbital electron, which combines with a proton to form a neutron. This also decreases the atomic number by one.1

Because the number of protons changes in each of these processes, the identity of the atom shifts to a different chemical element.13