What are the signs the Jews will look for to know that the Messiah has come?

Your question about identifying the true redemption is what brought R. Abba and his fellow rabbis about 1,600 years ago (Sanhedrin 98a) to search for the “revealed/clear sign/time” of redemption - that is, as opposed to many of the other signs mentioned by the prophets which are unclear or "unrevealed". They answer: "There is no more 'revealed/clear sign/time' than that which is written (Yechezkel 36, 8), 'And you, mountains of Israel, give forth your branches, and carry forth your fruit, for My Nation of Israel is coming/returning soon'. Rashi explains that when the Land of Israel (barren for so long) will return to produce fruit abundantly, that is the clearest sign that the return of the Jewish Nation is near. The flourishing modern Land of Israel, barren just 100 years ago, speaks for itself! (see photo of Tel Aviv 100 years ago and compare here) In addition, the Talmud (Megilla 17a) explains that the second stage of geula, after the fruitful revival of the Holy Land, is the mass aliya, “kibbutz galuyot” (= the national return to the Land of Israel). The prophecy says: “the third (time) they shall remain in her (in the Land)’ (Zechariya 13, 8), upon which the Oral tradition (Midrash Tanchuma P. Shoftim 9) explains: that Israel will only resettle in their land in the third redemption. The first redemption is the redemption from Egypt, the second redemption is the redemption of Ezra (the Second Commonwealth), the third has no end”. Note that the negative language used here, both at the beginning (“will only (!) resettle in their land in the third redemption”) and at the end (“has no end”) is much more definite than other less clear, signs of redemption. In Yalkut Shimoni (Hoshea, 518), the rabbis clarify that the number of Jews in the final redemption will be 600,000, after which, as we have seen, there will not be another exile. Today, with about 7,000,000 (!) Jews in Israel (more than 100X the amount in the second return: 42,360), we have clearly experienced that second sign, from which the rabbis taught us, there is "no turning back!" Statistically, by the year 2020, most (!) of world Jewry will reside in Israel, for the first time since the exile of the ten tribes almost 3,000 years ago. Thirdly, the Rambam (Maimonides, Teshuva 8, 7; 9, 2, based upon Brachot 34b) defines the "days of Mashiach", as when Jewish sovereignty returns to Israel, as we see in today's Jewish State, for the first time in 2,000 years. Regarding the Mashiach himself, the Talmud (Megilla, ibid), tells us that he will come only at a later stage of redemption, and the rabbis of that generation will let us know that it’s him. In summary, none of the "false messiahs" ever fulfilled any of these, and yes, we are clearly in the period called “y’mot haMashiach”, the days of Mashiach, whose pace and completion depends upon us and our actions, returning to the Land of Israel and strengthening our Torah observance. With Love of Israel, Rabbi Ari Shvat