A lot of people go looking for free links and end up spending days on techniques that stopped working ten years ago. Worth separating them.
Works
Catalogues and search sites in your field
The test is the relation to your subject. A restaurant directory linking a restaurant makes sense to the reader and to the search engine.
Associations and professional bodies
Trade associations, professional boards, cooperatives. They tend to have old, respected sites, 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 sector, portfolio pages. Many of those links do not pass reputation directly, but they help you be discovered — which is the first problem of every new site.
No longer works
Comments on other people's blogs
It was common fifteen years ago. Today those links are marked in a way that passes no reputation, and the effort does not pay for itself.
Forum signatures
Same case. And forums that allow the practice tend to have low reputation.
Directories that accept anything
If the directory has no defined subject and accepts every site that turns up, it says nothing about you. A link from a place that links everyone is not a recommendation.
The difference between free and cheap
A legitimate free link costs time: researching, submitting, waiting for approval. A "cheap" bought link costs money and can cost you rankings later.
There is an honest middle ground: a service that does the submitting for you, on sites related to your field. That is what Magneth does — more than 100 search sites in the network, with the listing inside related content.
On what separates a good link from a bad one, see what are backlinks.