"Находиться" (which literally means "to find itself") is a catch-all word that means "to be situated" or "to be located". It's not as formal or dry as the English translations, but still a bit formal. As for "лежать" vs. "стоять", I can only provide you with the basic guidance. If it's something flat or shapeless and is placed more or less flat on a horizontal service - use "лежать". Also, if you would naturally use the verb "to lie" in English - use "лежать". For everything else, "стоять" would be your best bet.
E.g. a bicycle propped against a wall - стоит.
The same bicycle lying on the ground - лежит.
А book sitting on a table - лежит.
The same book placed vertically on a bookshelf - стоит.
Btw, it doesn't bother you that things like books can actually be sitting in English? Think about it next time you get frustrated with the Russian choice of verbs ;-)
Thank you! On a side note, about Находиться and other reflexive verbs, I am amused and surprised in how similar some of these verbs are to Spanish. As you just explained, Находиться literally translates to "find itself", and in Spanish there's literally the same reflexive verb with the exact sama meaning: "encontrarse". I wonder why this is, since these languages are not related at all.
Well, it is not true that they are unrelated - both belong to the same Indo-European family meaning they share the same ancestor. German, another Indo-European language, yet in a different group (i.e., it's neither Slavic nor Romance), also has the same "find itself" construction - so this might be some ancient common trait.