The gemara in pesachim 87b comments (translation and sumamry from dafyomi.co.il)
(R. Elazar): Hash-m exiled Yisrael among the nations in order that converts will added onto them - "U'Zratiha Li ba'Aretz" - one plants a Se'ah only because he expects to reap many Korim (a Kor is 30 Sa'im. See note in Appendix)
(k) (R. Yochanan): We learn from "V'Richamti Es Lo Ruchamah [v'Omarti l'Lo Ami Ami Atah]" - people that were not My nation will become my nation.
I don't know if this describes what the actual practice was, but Avraham Avinu proselytized
This website uses sources from the christian bible to show that seeking converts to Judaism was a common practice. I read a reference to the avot d'rebbi natan which says that Abraham and Sarah were active proselytizers but I couldn't find the quote in the text.
Also, consider the final 3 paragraphs of this article which state that according to the mishna (though the site gives no source) it was the responsibility of all people to spread Abrhamic monotheism.