AvatarPlus Settings

You'll find two options in this section. To show an additional field for social networks with your comments form, tick the check box Extra field. This field will be used by your visitors to enter the link to their social network profile from Google+, Facebook or Twitter.
In some cases it's better to just show the default field for the Homepage-URL and use the option to add an additional field. If you're using the Homepage field as your new social network profile field, the plugin will grab the visitors avatar from there.
If the visitor didn't enter any data (no matter which of the above mentioned options you've chosen), then the plugin falls back to either the Gravatar service if the entered mail address is registered there or your installations default avatar for comments.

AvatarPlus is capable of getting around redirects and working with Short-URL services like bit.ly or goo.gl

To use as less of your servers resources as possible, the plugin uses a simple caching mechanism. It saves the direct URLs to the profile pictures alongside the comment data (but not the profile picture itself). Tough this is a pretty slim and efficient way of saving data temporarily, it is recommended to clear the cache from time to time.
It doesn't make too much sense to save this data for really old posts which doesn't get read very often. This data can be safely removed as it just increases your backup size.
For the sake of slim and fast updates, AvatarPlus offers the possibility to remove cached after a given period of time. Just enter a value into the text field and select a unit (Day(s), Week(s), Month(s)) after which the data expires and the plugin can care about removing it. If you don't want to remove the data, just enter a Zero (0) into the text field. The selection doesn't matter in this case.
Please note that saving personal data of a visitor of commentator can bring up legal problems in some countries. The judicature of some countries require to delete saved data after a given period (if you're unsure what the situation is in your country, please consult a lawyer). Some legal systems also force to notify a user that your site is saving personal data. In this case you should also tell your commentators what exactly and for how long your saving the data.

Google+ Settings

You need an API-key from Google to use profile pictures from Google+.

You can get more information about how to retrieve such a key in the developer manual provided by Google here.
After you've obtained an API-key for your installation, please enter it into the text field for the Google+ API-key.