Here are the pages in the first two editions (second is more clear):
What he means to say is that the לחן, or melody, is to the tune of the Arabic ייא ראבי שאלים שאילמי in the mode of ראשט. So if you know how to sing ייא ראבי שאלים שאילמי you're good to go. In case this isn't clear, it would be like the instruction to sing אשר ברא to the לחן of לאנד דאוון אנדר only in this case it would אוסטריליאש rather than ערעבי.
Najara's hymn book is full of instructions of this sort. The melodies are not only Arabic, but also תורקי (Turkish), Spanish and Greek. Almost every song is written to be sung to some kind of non-Jewish tune. In the introduction he writes that his purpose is basically to provide Jewish, religious songs for the youth.
It should be noted that he didn't know dozens and dozens of gentile songs by accident. He spent a lot of time in environments where he learned these songs, which was not lost on contemporaries who did not consider it a particularly pure pastime to hang out in clubs all night, so to speak. R. Chaim Vital wrote that it's true that his songs are alright, but he was drunk all the time. He also accuses R. Yisrael Najara of homosexual behavior, and of sleeping with a married woman. And cooking on shabbos.
Whatever anyone thinks of this stratagem (and/ or the sincerity of the author) he was hardly the first to try his hand at writing religious Jewish songs meant to be sung to non-Jewish tunes. We generally know about the practices from its condemnation. So, for example, the great Masoretic scholar R. Menachem di Lonzano doesn't mind the idea of singing the Jewish liturgy in synagogues to non-Jewish songs, but he is bothered by the idea of specifically writing a Hebrew song with the words meant to correspond with a secular gentile tune in the form of sound alikes. The example he gives is how the words שם נורא sound just like the word signora (שתי ידות [Venice 1618], pg. 142a). It's unclear to me if he is talking about an actual song, or a potential one. In the next paragraph he goes off on R. Yisrael Najara.
Possibly the most notorious user of this technique was famed 18th century Sabbatian Trinitarian Kabbalist Nechemia Chiya Chayon, who seemed to have been particularly fond of the consonance between "La Bella Margherita," a popular Italian song about a beautiful woman named Margaret ("as white as a flower"), and the Aramaic phrase "לא באלהא מרגליתא." His ditty, to be sung after reading the Zohar and Idra, begins like this:
לא באלהא מרגליתא בפום דכל בר חי
כי אם בפום רבינו הוא שמעון בר יוחאי
Or at least that's what his opponents said. He himself did not deny it, but pointed out that this is something that Jews do all over the Ottoman lands where he was from. Here is the verse, at the end of his רזא דיחודא: