How do I share apps between users in Android 5 Lollipop? I got a Nexus 9 tablet that I'm sharing with my wife. 

I set myself as owner and set my wife as another user. 

How do I give the other user access to some of the apps I have installed, without re-installing the apps in the other user space?
You reinstall the app, but they use the same install with different data, so the apk isn't downloaded twice (when you click install on a app that is already installed for the other user you will notice it is quite quick). So they already use the same app.

However if you want to share data, you could use one local account, or log in  both yours and your wife's local account into the same account for whichever service you wish to share.