How do people manage their Continuing Education requirements? Any tips on how to stay organized?

Have a spreadsheet and include when, what, title, and number of CE. Link to the listing. Sign up for CE that are interesting, year round, not just hurry up to get it at the minute.

Join a professional org to get unlimited CE offerings from them.

I find a lot of my online CEUs through NSO (which is where I get my malpractice insurance). As already mentioned, make sure that you organize your CEUs on a spreadsheet (Excel works quite well).