How to insert Google Tag Manger

For what? Measuring the use of Mailwizz or the sites where the landing pages link to from Mailwizz sendouts?

Anyway: copy the code snippet from the Google Tag Manager container and paste it into the site you want to add tag manager to, e.g. you can use it like you use Google Analytics, that is, paste in the tag manager code where the GA code should be and let tag manager contain the GA tracking instead.