"The woman wears a ring."
Translation:האישה עונדת טבעת.
Or unless you're a פסיקופת - combining words of "comma" (,) and "psychopath" to describe "crazy about language", a Hebrew version of grammer nazi, though many people say גרמר נאצי - this is mainly due to the great difficulty for Ashkenazim to express ע (as well as ח) in a proper manner, and accordingly, to the poor learning of language.
about ט or ת; if it is a loaned word, that depends on the spelling of the original word, 'th' would be transliterated to "ת", and 't' would be transliterated to "ט" (for example, the word mathematica is transliterated to מ-ת-מ-טי-קה). the same goes for names.
if it isn't a loaned word, that depende on the word itself and it's meaning (a bit like the differences between g and j or k and q), unless of course it is a suffix, and then it will always be writen with ת (for example, the noun אהבה becomes to אוהבת (fem. singular) and אוהבות (fem. plural)).
the differences between א and ע are more complicated, and are expressed in their different consonants. א express a closed glottal plosive phonating (/ʔ/), while ע express a voiced pharyngeal fricative (/ʕ/) - I hope that I translated it correctly - so it is more like the differences between a and e (though these days most people do not pronounce correctly those differences).
This was long ago; I later figured out a way related to Arabic.
..I happened to come across a list on Wikipedia. It compared the pronunciation of letters in old hebrew and modern hebrew. I got to know that ט is the archaic tough form of ת, (like the Arabic ط (tuh) which is a tough pronunciation of ت (ta) ), and that ע is a voiced pharyngeal fricative, used long ago in hebrew to sound as the arabic "ayn" ع , but now pronounced as א, the glottal stop. By comparing the hebrew word with its similar Arabic word which shares with it the same meaning or root word, I developed a way to make me know when to use either letters.
For Example, the word: טעים
It is similar to the word "ta3m" (طعم ) in arabic. While I know that the "t" in ta3m is a tough "t", and that the voiced pharyngeal fricative represented here by a "3" is an Arabic "ayn" , I know and can always remember that I should use the ט, not the ת, and the ע, not the א.
Ha-isha onedet taba'at. Onedet : עוׂנֶדֶת So, each letter with nikud/diacritic is a syllable. SEE JBS Hebrew, episode 3, starts around 4:30 : https://www.youtube.com/playlist?list=PLFYVdHvwACGu0b-foW7PDLuMfFAb6dUPV