Question

When do you use δοκιμάζω and when προσπαθώ?  For example, how should I say, "I am trying to speak Greek"?

Answer 1

"δοκιμάζω" means :  test, taste, try out, try on, attempt.  There is no effort involved here.  Examples:

Δοκιμάζω να ξεκινήσω το αυτοκίνητο, αλλά μάλλον δεν έχει βενζίνη.

Δοκιμάζω ένα ρούχο, να δω αν είναι στο μέγεθός μου.

Δοκιμάζω το φαγητό, να δω αν έχει αλάτι.

"προσπαθώ" means attempt or try.  I am putting an effort in the process. Examples:

Προσπαθώ να διαβάσω για τις εξετάσεις.

Προσπαθώ να σηκώσω ένα βάρος.

Προσπαθώ να τον πείσω να αλλάξει γνώμη.

"I am trying to speak Greek" would translate to "Προσπαθώ να μιλήσω Ελληνικά".  Meaning I have learned some Greek and I am trying to use them.  It is a rather difficult task for me but I am putting an effort to do it.

However, if you are a fluent Greek speaker visiting a shop in NY  owned by Greeks and I told you "Try to speak Greek there", it would translate to "Δοκίμασε να μιλήσεις Ελληνικά εκεί".  So this would be a test, you would speak Greek to see if anybody could speak Greek back to you.  There is no effort involved.