Hi.
You need to download the pangu tool for iOS 8.4, you need to google for this one.
Make sure it's the right version and download it.
Before you jailbreak, please make sure that you have a backup of all your files, calendars, contacts and so forth, you can create a backup directly in iTunes or in iCloud.
To jailbreak, you need to turn off the find my iPhone feature and your touchID or passcode if you have it enabled in the first place..
I am not sure if you need to deactivate anything else, so please look it up on google to get perfectly sure on what you are doing.
Then, plug the device in to your USB slot on your machine and start pangu.
The following windows are inaccessible to screenreaders, but there is still a way to jailbreak your device.
press the tab key three times and hit space bar. This deactivates a checkbox for some kind of pirated appstore. I wouldnt install it. The JB comunity reports this appstore as buggy and dangerous to your device.
After hitting space, hit tab one more time and hit enter. If all went right, the jailbreak procedure should start.
I don't know if you have to do anything after that. In the new jailbreak tool for iOS 9 you have to activate a pangu icon on your iPhones homescreen, but I am not exactly sure how it did work with iOS 8.4, even though I jailbroke it a few months ago.
So please, please! recheck guides on google how the exact procedure works.
I hope I could help you at leased a bit.
If you have more question of that matter, just ask and I will try to help you out.
I jailbroke devices since iOS 4.3.3, so I guess I know some things about jailbreaking, (No intend of bragging here.)
Greetings Moritz.