Hi,
Take a look at the Gretl User's Guide accessible via the menu "Help ->
User's Guide".
Or look here:
https://sourceforge.net/projects/gretl/files/manual/gretl-guide-a4.pdf/do...
Search for the keyword "modtest" in the guide and you'll see how to conduct
specification tests after having estimated some model.
Quick overview about the modtest command:
https://gretl.sourceforge.net/gretl-help/cmdref.html#modtest
I also recommend Lee Adkin's book where you find many applied examples:
https://www.learneconometrics.com/gretl/index.html
By the way, some time ago we've started to translate the FPP book examples for gretl:
https://github.com/gretl-project/forecasting_principles
However, not all chapters and examples are covered, yet.
Artur