From the Gemora here about a ball tefilla making a mistake in davening and being replaced, it is understood that in the time of the mIshna they davenned by heart with no siddur. Similiarly, previously in the Gemora when Shmuel haKoton had forgotten the nusach of Velamalshinim - it seems it was not written down. The reason being only Tanach Torah Shebiksav was written down and davening was considered Torah Shebaal Peh. This sheds light on Chazal being mesaken Chazoras HaShatz for those who did not know how to daven. This includes not just people who could not read, but also those who did not know the Shmone Esre by heart. Indeed, iIt would have been very difficult to learn Shmone Esre by heart if there was no written text to memorise.
Later R' Yehuda HaNasi saw a need to write down the Torah Shebaal Peh and wrote down the Mishna. When was the first Siddur written? Was it at the same time or later?
Yisroel Alter Pacanowski, Melbourne, Australia
The first recorded Sidur was Seder Rav Amram Ga'on. The Nusach of the Tefilah depended on the affiliation of each scribe who copied it. Why, though, until Rav Amram, was the Sidur not recorded? The Seder ha'Tefilah of yore was that the Shali'ach Tzibur was appointed to recite the Tefilos on behalf of the people. Besides all of the other qualifications, he had to know the Tefilos by heart. To give an example, the Shali'ach Tzibur would say Birkos ha'Shachar in this fashion: the Shali'ach Tzibur would say the first Berachah, the Tzibur would answer Amen, and then the Tzibur would repeat the Berachah, and so on. The Shali'ach Tzibur would say the Tefilos aloud and the Tzibur would follow along. For that reason we find Piyutim which were said only by the Shali'ach Tzibur and the Tzibur would answer a short reply (such as the Piyut of Melech Elyon said on Rosh Hashanah, where the Tzibur says Melech Elyon at the beginning of each stanza and the Shali'ach Tzibur then says the Shevach which describes Melech Elyon).
When putting the Sidur in writing became permitted because of "Es la'Asos la'Hashem," copies proliferated, and the general populace became proficient in the Tefilos. The invention of the printing press accelerated that process, so that today everyone knows the Tefilos. (You can find in Teshuvos Radvaz that even in his time there were still people who could not Daven, as he addresses the question of whether they may rely on the Shali'ach Tzibur to be Motzi them with Chazaras ha'Shatz.)