Great. Phrasing it that way, you’ll want to put “dive” into the past tense. You can either use “dove” or “dived” – both are acceptable (“dove” is more popular in North America). So you can say: “I got down to business and dove into the details.”

Thank you, I rewrite: In the meeting, I thanked everyone who arrived. I got down to business and dived into the details.

This is very good – just the last part needs a little work. You don’t “start” details. You can “start to describe” details or you can “dive into the details” (meaning, start talking about the details).