I am looking for a way to recognize members of the Beth Shammai and Beth Hillel when I learn the gemara and mishna. I need to know when the Beth Shammai ended (as well as the Beth Hillel) to find out if the amoraim quoted in the Gemara were members of one of these two schools or if they were members of no school.
Hillel and Shamai themselves were the last of the Zugot -- pairs of scholars who served as the Nasi (prince) and Av Beit Din (chief justice), respectively. The Zugot are listed in the first perek of Masechet Avot (Pirkei Avot).
The Steinsaltz Talmudic reference guide contains a nice chart listing the generations of Tannaim and Ammoraim. According to it, the first generation of Tanaaim is from 20-40 CE. This is immediately after the period of Hillel and Shamai, so it stands to reason that Tannaim from this generation participated in one of their academies.
However, the chart lists very few Tannaim as being from this generation. (I found Rabban Gamliel Hazaken, Akavya ben Mehalalel, Rabbi Yonatan ben Uziel, Bava ben Buta, and Bar He He skimming down the list.) My guess is that most of the other scholars were part of the two schools, and did not express many of their own opinions. After the schools ended, we see a lot more from the following generations.
Just because a sage was not in either academy doesn't mean he doesn't follow one or the other, however. Mishna Brachot 1:3 tells a story about Rabbi Tarfon (3rd generation) who followed Beit Shammai, and nearly died because of it. I also remember the Gemara on occasion saying that certain Amoraim held like Beit Shammai in certain cases. The majority of sages, however, followed Beit Hillel. Beit Hillel had more members, and was also more lenient, which was easier to adopt than the stringent practices of Beit Shammai.
So, to summarize: The schools ended in approximately 40 CE, at the end of the first generation of Tannaim. However, their influence continued to last throughout the Tannaic and Amoraic periods. Most sages support Beit Hillel, because that's who we pasken like.