In recent centuries, authorities such as the Chazon Ish, Rabbi Chaim Na'eh, and Rabbi Moshe Feinstein ruled on the exact size of a tefach, ammah, kezayit, and other shiurim. What did people do before these rulings? Did they just estimate the size of their own hands, or was there an unwritten tradition of some sort?
The Mishna in Keilim discusses this. Essentially they guessed it, based on the average measurement.
Starting from Ch. 14:5, here are some of the measurements:
פרק יז - משנה ה: הָרִמּוֹן שֶׁאָמְרוּ, לֹא קָטָן וְלֹא גָדוֹל אֶלָּא בֵינוֹנִי
The pomegranate [mentioned in previous Mishnayot] refers to a medium sized one. [Presumably a fully-ripe one.]
פרק יז - משנה ו: כַּבֵּיצָה שֶׁאָמְרוּ, לֹא גְדוֹלָה וְלֹא קְטַנָּה אֶלָּא בֵינוֹנִית. רַבִּי יְהוּדָה אוֹמֵר, מֵבִיא גְדוֹלָה שֶׁבַּגְּדוֹלוֹת וּקְטַנָּה שֶׁבַּקְּטַנּוֹת, וְנוֹתֵן לְתוֹךְ הַמַּיִם, וְחוֹלֵק אֶת הַמָּיִם. אָמַר רַבִּי יוֹסֵי, וְכִי מִי מוֹדִיעֵנִי אֵיזוֹהִי גְדוֹלָה וְאֵיזוֹהִי קְטַנָּה, אֶלָּא הַכֹּל לְפִי דַעְתּוֹ שֶׁל רוֹאֶה:
An Egg-size refers to a medium size. Rabbi Yehuda says one brings the biggest one can find and the smallest one can find, puts them in a vessel full of water, and then one divides the spilled water. Rabbi Yossi says one uses one's best estimate of what seems to be an average size egg.
פרק יז - משנה ז: כַּגְּרוֹגֶרֶת שֶׁאָמְרוּ, לֹא גְדוֹלָה וְלֹא קְטַנָּה אֶלָּא בֵינוֹנִית. רַבִּי יְהוּדָה אוֹמֵר, הַגְּדוֹלָה שֶׁבְּאֶרֶץ יִשְׂרָאֵל הִיא הַבֵּינוֹנִית שֶׁבַּמְּדִינוֹת:
A fig - refers to a medium sized one. Rabbi Yehuda says that the big ones in Israel are like the medium ones elsewhere.
פרק יז - משנה ח: כַּזַּיִת שֶׁאָמְרוּ, לֹא גָדוֹל וְלֹא קָטָן אֶלָּא בֵינוֹנִי, זֶה אֵגוֹרִי. כַּשְּׂעֹרָה שֶׁאָמְרוּ, לֹא גְדוֹלָה וְלֹא קְטַנָּה אֶלָּא בֵינוֹנִית, זוֹ מִדְבָּרִית. כָּעֲדָשָׁה שֶׁאָמְרוּ, לֹא גְדוֹלָה וְלֹא קְטַנָּה אֶלָּא בֵינוֹנִית, זוֹ מִצְרִית. כָּל הַמִּטַּלְטְלִין מְבִיאִין אֶת הַטֻּמְאָה בָּעֳבִי הַמַּרְדֵּעַ, לֹא גָדוֹל וְלֹא קָטָן אֶלָּא בֵינוֹנִי. אֵיזֶה הוּא בֵינוֹנִי, כֹּל שֶׁהֶקֵּפוֹ טָפַח:
- Olives: Medium - i.e. Egori ones.
- Wheat kernel: Medium - i.e. Midbari ones
- Lentil: Medium - i.e. Egyptian ones
- Thickness of cattle prod: Medium - i.e. circumference 1 Tefach
פרק יז - משנה ט: הָאַמָּה שֶׁאָמְרוּ, בָּאַמָּה הַבֵּינוֹנִית.
Ama - arm's length - medium.
I heard the following from Rabbi Heinemann, in answering this question (specifically he was asked about R' Moshe's teshuva about the exact height necessary for a mechitza, which has a dearth of prior literature on the subject):
There is a famous story in which the Chofetz Chaim was upset because his children wanted to put a floor in his house (which had a dirt floor). He said "next thing you know you're going to want a clock!" What did the Chofetz Chaim have against getting a clock? If you don't have a clock, you err on the side of caution - you don't wait until the last minute to daven or to bentch licht, you make sure you do it well before you get into a period of uncertainty. In generations where they didn't have the ability to measure with more precision, they were much more careful - they knew an approximate amount, and they made sure they were safely within that range.
R' Heinemann suggested that it is really a testament to the lowliness of our generation that we have everything calculated out to the nth decimal point - because we are figuring out the least we have to do to get by. Once upon a time, they made sure that they got it right by going beyond the exact minimum/maximum.