Plenty of people go looking for free links and spend days on techniques that stopped working ten years ago. It is worth separating them.
Works
Directories and search sites in your field. The test is topic match. A restaurant directory linking a restaurant makes sense to the reader and to the search engine.
Associations and professional bodies. Chambers of commerce, professional councils, cooperatives. Their sites tend to be old and respected, and listing members is natural.
Partners and suppliers. The easiest link there is, and the most forgotten. You just have to ask.
Professional profiles. LinkedIn, profiles on platforms in your industry, portfolio pages. Many of those links pass no reputation directly, but they help you be discovered — which is every new site’s first problem.
Does not work any more
Comments on other people’s blogs. Common fifteen years ago. Today those links are marked so that they pass no reputation, and the effort does not pay.
Forum signatures. Same case. And forums that allow it tend to have low reputation themselves.
Directories that accept anything. If a directory has no subject and takes every site that shows up, it says nothing about you. A link from somewhere that links everyone is not a recommendation.
Free is not the same as cheap
A legitimate free link costs time: research, a message, a follow-up. What is sold as cheap usually costs reputation instead — and that is a far more expensive currency.