How do I know when to use the preposition "je"?

Question

The word "je" seems to be randomly used. It's meaning, I understand, is somewhat undefined, although it does seem that it can be used in place of the accusative in some cases. If you look it up in the dictionary, it shows multiple definitions:

From Lernu.net

je (je) upon, at, by, on

How do I know when to use it? Is it something I just have to memorize?

Answer 1

On The Sixteen Rules of Esperanto, I found the following description for je.

Every preposition has a definite and permanent meaning, but if we have to use a preposition and the direct meaning doesn't tell us what preposition we should take, then we use the preposition je, which has no independent meaning. Instead of je the accusative without a preposition may be used.

The followed examples are used.

Li vetas je la ĉevaloj. (He bets on the horses.)
Mi alvenos je la oka horo. (I'll arrive at eight o'clock.)
Li vizitos nin je lundo. (He'll visit us on Monday.)

As alternative for the last sentence, Li lundon vizitos nin. is given.

Je is used when you need a preposition, and none of the other prepositions can be used.

There is also the following note.

Since this rule gives us permission to use the -n ending instead of the preposition je, some Esperanto speakers also assume that it permits us to use the preposition je instead of the -n ending. This is a convenience when we encounter a word (such as a proper name) which doesn't lend itself well to taking a regular Esperanto ending.

Mi ja konas Glazunovski-on. (I do know Glazunovski.)
Mi ja konas je Glazunovski.

Answer 2

Estas 3 kazoj en kiuj oni uzas ĝin (fontoj sube).

Tempo/mezuro (kiam? kiom?).

Kiam? (je ĵusta horo. Punkto en la tempolinio. NE periodo!)

• Mi vidis ĝin je la naŭa. = L'ho visto alle nove. (A che ora/data? In che occasione?)

Kiom? Kvanto.

• Ŝi estas je kvin jaroj pli juna ol mi. = Lei è di cinque anni più giovane di me. (Di quanto?)

Malklaraj rilatoj - kazoj malofte uzataj (ĉu krei preposicion nur pro tio?) - ĉiam temas pri specifado de adjektivoj, verboj:

• Havi soifon je povo. = Aver sete di potere. (Complementi che non hanno una preposizione apposita)
• Dieto riĉa je vitaminoj. = Dieta ricca di vitamine. (Aggettivi che quantificano qualcosa: carente di, abbondante di...)
• Je Jovo! = Per Giove! (Complementi che non hanno una preposizione apposita)

Se vi konas la italan, ĉi tie estas ekspliko gramatike pli ĝusta. Se vi komprenas ĝin, vi komprenos la preposicion "je":

1. ĝenerala: https://it.wikibooks.org/wiki/Esperanto/Preposizioni#La_preposizione_je

2. pli profunde: https://it.wikibooks.org/wiki/Esperanto/Approfondimenti#La_preposizione_je

Estas aliaj klarigoj en interreto, sed tiu estas la plej facila kaj bona.

Answer 3

Je is the fallback when nothing else works.

When no particular choice of preposition was obvious from the sense, the generalized preposition je was to serve. In actual practice, je is surprisingly rare. http://pages.ucsd.edu/~dkjordan/eo/colloq/colloq050.html