In Telegram, find the New Group button:

Select at least one group member from your contact list (you can add @InviteMemberBot aka InviteMember) and hit Next. 

Now you can enter your group's name and set your group's photo (if you don't have a logo, you can get a free photo/icon from websites like unsplash.io and iconfinder.com). When you're ready hit Create.

Done!

Did this answer your question?