I've learnt that acheter becomes j'achète, tu achètes, il/elle/on achète in present tense conjugation. However, the word jeter, which looks like it has exactly the same construct as acheter(in terms of vowels and consonants order), instead of being conjugated as je jète, tu jètes, il/elle/on jète, it conjugates as je jette, tu jettes, il/elle/on jette. This is very confusing. When one encounters a new verb that has similar structure like acheter and jeter how could one tell which way to conjugate?
The phonetic value of the letter e which could represent the sounds [ә], [e] or [ɛ] has been a lasting ambiguity that has established itself over the centuries. This is an inheritance of the Latin writing system and of the French specific sound changes that occurred over the time. Various devices were used in the course of history to try to disambiguate the situation, the most important one before 1990 was probably the introduction of accents in the 16th century.
Until 1990 there were quite a lot of inconsistencies in the use of accents and how they related to pronunciation. The 1990 orthography reform was a great step towards unification, but... there is a "but".
The 1990 orthography reform recommends that [ɛ] be always spelt with è in -eter and -eler verbs (that was already the case for some verbs but not all). But after long debates two exceptions were allowed: for the verbs jeter and appeler (and their derivatives), it was said, their spelling had long been stabilised.
When one encounters a new verb that has similar structure like acheter and jeter how could one tell which way to conjugate?
Acheter is the rule, jeter is an exception1. When in doubt you can check a conjugation table online, and although the 1990 reform was not made compulsory until 2008 in school curriculum and schoolbooks for every use both spellings can be used.
1 Would the French language still be the French language it there weren't any exceptions (tongue-in-cheek statement).
This is not a matter of conjugation; the conjugation is the same (e, es, e, ons, ez, ent). What is changed is, so to speak, the orthographic implementation of the sound "è": "è" and "ett"; those two spellings, because the t is doubled, have the same sound (which is that of "è"). So, the proper question, which you can ask on another post, is "Why in the conjugation of "acheter" and "jeter" is the sound "è" rendered by different spellings?".
It should be said that the sound of "e" is changed from "e" to "è" because in the next syllable the vowel is again "e", and two consecutive e's make for an awkward pronunciation, but that is not really a matter of conjugation; it is merely caused by it.