How did certain words become homonyms?

Several ways. Dimitra Triantafyllidou has already answered; I’ll answer as well, a little more schematically, but it’s essentially the same answer.

• Sound mergers in the language. meet and meat used to be pronounced differently [meːt, mɛːt]; now they’re pronounced the same, [miːt].
• Sound un-mergers in the language—or at least, a spelling system out of sync with pronunciation. I read it now, I read it yesterday: same spelling, different pronunciations [ɹiːd, ɹɛd]. I’ll include here stress splits like désert (noun)/desért (verb).
• Borrowing into the language from two different origins; e.g. Dimitra’s example of tire, French and Germanic.
• Zero derivation: English can form verbs from nouns without adding any extra affixes. E.g. a book, to book.
• Semantic split (polysemy). What used to be a single word is now considered two different words, because of diverging meanings. Crane as in bird; crane as in machinery.