For example, you want to get query parameters from URLs like this:
www.mystore.com/search?q=shoes&color=red

To simplify the process I use Google Sheets as a data source. But you can use raw data from Google Analytics as well:

When we have this data in Google Data Studio our goal is to have query parameter as separate columns in our report like this:

To do this we have to create, a new field, and use REGEXP to extract the data from URLs:

In code below "q" is the query parameter you want to extract for example "color":

REGEXP_EXTRACT(URL, 'q=([^&]+)')
~~~~

If you use Google Analytics as a data source, change the URL with PAGE dimension:

REGEXP_EXTRACT(Page, 'q=([^&]+)')
~~~~

Now we can create reports based on new fields: