Sharepoint - How to see what site template is used in SharePoint Online (Office 365)

On your site, view the source of the start page (ctrl + U) and search for JavaScript variable g_wsaSiteTemplateId.

You'll get the Template ID like this

var g_wsaSiteTemplateId = 'STS#0';

Then just find what template that is in the list presented in the article SharePoint 2013 Site Template ID

I've been trying to find out why when I search the Source Code from my 365 tennant I can't find a 'g_wsaSiteTemplateID' variable anywhere. It seems like the variable name has been changed to 'webTemplateConfiguration'.

I found my Template ID looking like this:

"webTemplateConfiguration":"STS#0",

The values don't seem to have changed though so you can still correlate what you find with mentioned article.