how do i find someone's email address by their name without a big budget?

For work contacts, the cheap route is guessing the company's pattern. Most use something like first.last or first initial plus surname at the domain, and you can usually work out which from one address published on their site or in a press release. Run the guess through a free email verifier before sending. Hunter's free tier covers a handful of searches a month if you'd rather not guess. Check their LinkedIn contact info too - some people leave it there. Keep it to business addresses though; digging up someone's personal email is where it gets creepy fast.