How do you know when you have to attribute the designer?

If you have to credit the designer, it will be specified in the license agreement (where it says License: ...). As a rule of thumb, licenses that have the word "attribution" in their names (mostly Creative Commons licenses) require crediting the designer. For other license types, crediting a designer is optional.

How to properly give attribution to the designer?

You can do this by including their name and a link to their website or to their Iconfinder page. Here are some examples of Best practices for attribution.

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