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.