Hello and welcome to Android Forums. Hopefully I can help you with your problem.
You are probably going to need to be rooted in order to access the files required to change the boot up sound. Without knowing what device you have, I would say there is a 99% chance that your device needs to be rooted. Just wanted to give you a heads up on that.
Without knowing the exact device you have, I am going to give you a basic answer to your question. You are going to need to locate where the boot up sound file is located and replace it with the new one you want. Make sure that the new one is the same sound format as the original sound file on your phone too or it will not play. Boot up sound files cannot be very long either.
I invite you to join Android Forums and search through your device's section. There's a very good chance you'll find all the info you need in there.