Hi Riaanuk, welcome to InfoPath and SharePoint :)
On the form where you will be doing search, you need to create a new data connection to your SharePoint list to receive data. After adding the new data connection you will find that there is a new secondary data source in your fields task pane.
I'm not sure if you need to search all columns in SharePoint list or a specific column but all those columns will be available in your secondary data source for you to search. Look at the function contains() and see if it could be useful in what you are trying to do.
That should get you started. Let me know if you need further help.
Jun