I recently made a music bot in my discord server but the problem I have is that I have to turn on the bot manually etc. and it goes offline when I turn off my computer. How can I make the bot stay online at all times, even when I'm offline?
You need to run the python script on a server, e.g. an EWS linux instance. 
To do that you would need to install python on the server and place the script in the home directory and just run it via a screen.
How do I make my discord bot stay online