how do i get backlinks without a big budget?

Unlinked mentions are the easiest win I know of. Search your brand name in quotes, find pages that already mention you without linking, and send a short friendly note asking if they'd add the link. The hit rate is decent because they clearly already like you. Same with images - if people are using your photos or charts, ask for a credit link.

The cheapest links that actually count come from being useful to someone with a site - suppliers, partners, local organisations you already deal with, trade bodies you're a member of. slow, but they're real. avoid anything sold as a package. what line of work is the site in?