The most common English word, "the," is a definite article used to refer to something specific that both speaker and listener know about, as in "the book on the table." It is followed by the indefinite articles "a" and "an," which introduce something new or nonspecific. The choice between "a" and "an" depends on sound rather than spelling: "a" precedes consonant sounds, while "an" precedes vowel sounds, so we say "an apple" and "an hour" (silent h), but "a university" (pronounced "you-ni-").
Demonstratives point to things by their distance from the speaker. "This" and "these" refer to things that are near (singular and plural respectively), while "that" and "those" refer to things farther away. When used before a noun, they function as determiners ("this book"), but as pronouns they can stand alone ("This is interesting").
Possessive determiners show ownership and agree with the possessor rather than the possessed thing: "my," "your," "his," "her," "its," "our," and "their." Note that "its" (possessive) and "it's" (contraction of "it is") are different words. Quantifiers indicate amount or scope: "all" refers to the whole, "some" suggests an unspecified amount, "any" appears in questions and negatives, "no" negates ("no answer"), "both" refers to two together, and "each" treats items individually. "More" and "most" indicate additional or majority quantities, "such" emphasizes a particular kind or degree, and "other" signals something different or additional.