Learn Turkish: Bu belgede bir hata var, ben düzelteyim. - There is a mistake in this document, let me fix it.

The verb root is düzelt- (to fix or correct). We add the 1st person singular optative suffix -eyim because the last vowel in the root is 'e' (following e-type vowel harmony). It translates to "let me fix" or "I will fix".

Since the suffix -eyim already means "let me", why is the word ben (I) used here?

You don't strictly need it! Because the suffix -eyim clearly shows who is doing the action, düzelteyim alone means "let me fix it". Adding ben just adds a little emphasis, like saying "let me fix it" (implying: instead of you or someone else doing it).

Why does the sentence use var for "there is"?

In Turkish, existence is expressed with the word var (there is/there are) and its opposite yok (there is not/there are not) rather than a direct translation of the verb "to be". So bir hata var literally translates as "a mistake exists".

What does the -de suffix do in belgede?

belge means document. The -de is the locative suffix, which means "in", "on", or "at". Since belge ends with an 'e', it takes -de to follow vowel harmony, giving us belgede (in the document).