Open @BotFather in Telegram and send the /newbot command.

Then, pick your bot name and username:

@BotFather will send you a unique string called bot token:

Keep this token secret! 

Your bot is now created. To set the bot's profile picture, send the /setuserpic command to @BotFather, select which bot you're working with, then an image when prompted:

To change the "about" text shown in the bot's profile, send the /setabouttext command:

Now, the bot's profile has an avatar and a short description in the "about" section:

You may also want to change the bot description (shown in the bot dialog before users click START). To do that, use the /setdescription command in @BotFather followed by your description when prompted.

Finally, you can set an image to be shown above your bot description, this image is called description pic and can be set up by sending the /setdescriptionpic command to @BotFather.