Open @BotFather in Telegram and send /newbot command. Pick your bot name and username:
@BotFather will send you a unique string called bot token:
Keep this token in secret!
Your bot is now created. To set bot's profile picture, send /setuserpic command to @BotFather followed by an image:
To change the "about" text shown in bot's profile, send /setabouttext command:
Now bot's profile has an avatar and short description in "about" section:
You may also want to change bot description (shown in the bot dialog before clicking START). To do that, use /setdescription command in @BotFather.