Android is releasing a new permission model with Marshmallow. A bit ago, we were searching, how things are going to change for us as developers. The change is, that now, permissions are going to be requested at runtime instead of being requested during an install. However, there are two things to know before diving deeper.
As long as you do not set the target SDK version to 23, you are fine - the Google Play store and Android are going to use the old permission model and there should be no need of changes on your side. The permissions are going to be requested during install time as before.
You are not going to need to do any changes, if all of the permissions that you are using are in a group of Normal Permissions. Normal Permissions are granted automatically during install time. If you use only these, there won't be any SecurityException during runtime regarding them. Also, users cannot revoke them as well.
For all the other things you are going to need to go through Permissions documentation to know how to handle requests for these permissions properly.