How to create a Telegram Bot and add them to a group
First of all, search for @botfather
:

then write something to open the menu:

Write /newbot
and follow the steps into the chat, choose a name and an username, it must end in bot
or _bot
:

Disable the privacy:

Now copy the access token and search for @grouphelp
, then paste it:

Now just create a chat group and enter to the group and edit it, change the group type to public
:

And add your bot created before as admin, in thin step we need i didn't find a way on Telegram web, so simplest way is to get your phone and do it there.

Done! An example that how you can use is writing a curl command:
curl -X POST https://api.telegram.org/bot51130xxx75:AAHxxxxxxxwgxYqPlAbWUxxxX4/sendMessage?ch