how do you generate a password on apple.com

There are "Safari Suggested Passwords" that you can enable by using iCloud Keychain. There is a decent walk through at the following link, followed by some information about iCloud Keychain by Apple.

http://www.cultofmac.com/235237/get-password-suggestions-using-icloud-keychain-a nd-safari-in-mavericks-beta-os-x-tips/

Frequently asked questions about iCloud Keychain - Apple Support

OS X does not have such a built-in mechanism. You will need to look for third-party software to do that or make one up yourself.

I believe you meant this for the OP, not for me.