The Earthmother is the goddess of nature and plants, and doesn't enjoy heroes cutting a safari-style path through her precious flora. The Earthmother is one of the most straightforward deities in the game to please, and in practice the one of the few which you can reliably go the entire game without ever incurring any penalty to piety. However, her boons are mostly useful to low-level characters and of little help to high-level characters, meaning most players will opt to convert out at a certain point.
The Earthmother is uncovered in a subdungeon to the South. Her subdungeon is completely revealed, filled with plants and level 9 "gardeners". Cut your way across the room to her altar to unlock her.
The only two acts that anger the Earthmother are destroying plant life and using the life-steal ability. The only act that pleases her is using the IMAWAL glyph (you can also use the plantation boon to gain piety). This makes her fairly easy to play; petrify stuff to gain piety, and leave her plants alone. Since most dungeons don't have any plants to begin with, and the Earthmother does not create very many, it's unlikely you will ever have serious issues before the time comes to convert out.
The Earthmother's best boon is entanglement, slowing every monster on-screen. Slowed monsters lose their first strike benefits, and also grant 1 extra XP when killed. For a mere 5 piety, this is a very good boon and one that you should almost always take.
Her vine form boon is quite useful for low-level characters, granting extra hit points and damage reduction. Against low-damage monsters such as meatmen, this can allow you to fight enemies three or four levels higher than yourself. However, these benefits do not scale with your level and they will be largely meaningless by the time you're level 10. Investing too heavily in vine form is not a very good idea.
The greenblood boon is more difficult to leverage, but can be somewhat useful in some circumstances. Corrosion ignores resistances, and works best when combined with attacks that deal low damage, such as knockback, fireballs, and monk attacks. However, the cost of greenblood increases rapidly so it's seldom worth purchasing more than a few levels.
The clearance boon allows you to request the Earthmother remove plants for you while simultaneously restoring some mana. This makes the Earthmother invaluable for fuelling a late-game spellcasting approach. Because her bonus doesn't scale based on max mana, it's most useful to characters with poor spellcaster skills who need a little bit of a boost in that regard. Dedicated spellcasters are better suited to pursuing other more potent combos, but will still benefit from this given the opportunity.
The plantation boon can be used to generate large sums of piety, and is particularly useful when converting into the Earthmother during the end-game. Keep in mind that using this boon will effectively preclude a conversion into Dracul, since those blood pools will no longer be available for him. If you intend to make such a conversion at some point, avoid plantation.
The Earthmother grants 5 piety for petrifying plants and other non-XP enemies, and 10 piety for petrifying XP-yielding enemies. Try to focus on using this glyph on 1st level monsters and avoid touching higher-level targets that could be worth lots of XP.
The general strategy with the Earthmother is to use a variety of her boons at a low cost, then either use IMAWAL or plantation to build up to 100 piety, activate the entanglement boon, and convert out of her religion. Converting into the Earthmother to use plantation and then spend your piety on clearance is a great "last-ditch" move, though typically less powerful than what can be done with the Glowing Guardian or Dracul. The Earthmother also makes a good "escape deity" choice if you just want to avoid taking further piety punishments. If there are no plants on the field and you don't have a life-steal ability, she will never punish you.
The Earthmother also has the least harmful desecration penalty on her altar, causing a mere 5 layers of corrosion. You can cure this with a burn cure potion, and it's not going to be a huge deal for a higher-level character anyway. This makes her pretty much the only deity who is routinely desecrated immediately after converting out, and one of the most frequent victims of desecration of any deity.