How to Tell Who Added a User to a Particular Group

if it is with in your group then click under Record -> Account(organization details). to know all users details. if its different group then search under Record -> Users

I didnot got your point please explain

if you want to know details on a particular user, the above options will work.

let me explain . I have a custom group name "Internal User". Some one added a user say "user1" to the group "Internal User". So i want this log history "which user has been added to a particular group by whom". Is there any options to view this log history from designer?

@akaprobham Afaik, until and unless you setup an application (such as "User and Group Management Application 16.1+" at http://bit.ly/2ahz2AP) that captures the data from a place(From Process in form of Action/Related Action but not from the 'People' tab in Designer) where you can capture the data and make updates in DB, you may not be able to obtain the data you want. In short it's not available OOTB and the application mentioned above should help you and you may try customising it to meet your requirements.