How do you quote an adage in English? For example, assume you are giving an speech and you want to add an adage. Do you say "there is a saying ..."? or "as they say ... " What are the best ways to bring smoothly an adage to your speech?
Your own suggestions are good. There is no formal way of doing it. It depends strongly on how you want to present the information or the general tone of your presentation. For example, I'm fond of quoting from Shakespeare and I often lead in with "As the Bard says..." or "As the Bard tells us...".
If your tone is confrontational (you're challenging something), then you might consider, "Some believe..." or "There are those who think/say..."
If your tone is accepting (you're supporting something), then you might say, "many believe..." or "we should remember..."
If I were to invent a rule, it would be... "keep it short."