Honoring the Earth Mother is one of the parts of the ADF ritual format that makes it ADF as it being a discreet offset of ritual, and the treatment of her as a being, is not found in many places.  The other thing that is interesting about this part is that there is little, if any, evidence of her in abstract being worshiped by Indo-European people.  They would worship their local land and fertility beings, often female, but not an abstract idea of Earth Mother.  We can say similar for her counterpart, the Sky Father.

This all comes from where ADF started, RDNA, the Reformed Druids of North America.  Here we can trace it to their two basic tenants which boil down to: 1. Nature is good.  2. Likewise, nature is good.  This though was more about worshiping your local nature instead of nature as an abstract.  Where we went from local and named beings to the abstract, I personally do not know.

That all being said, we do have a variety of ways people call on the Earth Mother and sometimes the Sky Father.  Some Groves, and Shining Lakes Grove is one that I know follows, or used to follow, the tradition of honoring their local spirits.  This would be their local goddess Ana.  Many others though call on her in the abstract.  Some groves have also added in a counterpart to her with the Sky Father.  Whispering Lake Grove is one that does this regularly.  They are also, as far I know, the people who brought this into the rituals first.

So, how do we honor her?  First we have to ask are we doing it abstract or a specific being.  If we are doing a specific being, you should first work with her on your own or in a small group and get to know her and what she wants.  This is good advice for any being that you want to worship.  Similar, if it's in the abstract, get out in nature and experience nature.  The offerings you make here are usually some kind of solid food such as apples, corn meal, grains, etc.  If you can, spread it on the ground, or do so as soon after the ritual as possible.  The other common tradition, at least when doing this in abstract, is to bend down and touch the ground with your hand.  I personally will kiss my hand and then touch the ground as kissing the ground can be a bit dirty.  For Sky Father, you want your offerings to go up into the sky, so offerings of oil or alcohol to the fire are great.

The rest is just writing a prayer for her (and him if you're doing Sky Father too).  A simple one I often use is:

Earth Mother!

You who surround and support us.

You are in full bloom, and we are reaping all you provide us.

We honor you at this time of harvest.

Without you, we wouldn't be here, and we honor you for that.

Accept these offerings as a token of our appreciation.

Earth Mother, Accept our Sacrifice

This was for a Lughnassadh ritual when everything is in full bloom and the harvest is going full speed.  What I like to do though is describe the season we are currently in and celebrating, remind ourselves that without her, we couldn't survive, and finally make our offerings.