Learn Turkish: Biz sucuğu yumurtayla pişiririz. - We cook the spicy sausage with eggs.

Two things happen here. First, we add the specific direct object ending (the accusative case) -u because we are talking about "the" sausage. Second, when a Turkish word ends in k and gets a vowel ending, the k softens into a ğ. So, sucuk + u becomes sucuğu.

Where is the word for "with" in yumurtayla?

The word for "with" is normally ile, but it usually attaches to the end of a word as -la or -le following vowel harmony rules. Because yumurta ends in a vowel, we must add a buffer letter y, making it -yla. Also, notice how Turkish uses the singular yumurta (egg) for the general concept here, while English naturally translates it as the plural "eggs".

Why does the verb pişiririz have "ir" in it twice?

The root of the verb is actually pişir- (to cook something). The second -ir is the aorist (simple present) tense marker, which we use to talk about general habits, facts, or routines. Finally, -iz is the "we" personal ending. So it breaks down as pişir + ir + iz.