Often, an Esbat is celebrated by getting together with a coven or a few friends and honoring the Goddess and then having crescent cakes and wine afterwards. Of course, for solitary people (like me) that's not what happens at all. Esbats are a good time to create a ritual (see the rituals page for pointers on how to create one). A ritual to honor the Goddess can be created, looking at Her in the context of the wheel of the year. For instance, if it is near Mabon, the Goddess is a bit more somber because Her lover is dying and She is also pregnant. This is quite a bit different from the Maiden Goddess at Imbolc, when She is young and innocent, and quite different from the fertile, robust, energetic and sexual Goddess that represents Beltane and Litha; one would not confuse these other aspects of the Goddess with Her dark Crone face at Samhain either. Some people prefer not to celebrate Esbats as if they are in context with the Sabbats, because they think that the way you think of the Goddess should not be directed by what the God is doing; as you may know, many Earth religions focus more heavily on the female aspect than the male and would resent having the Goddess thought of in terms of the God's life cycle. However, I see the God and Goddess as just the whole of creation, and if my world is growing colder as winter approaches, I'm going to celebrate slightly different than if I am in the heat of summer.
A VERY common thing to do on Esbats is to work magick. Some people
consider the Esbats the best time for magick (and in some cases "Esbat"
just means any gathering that isn't a solar holiday). And this makes
quite a lot of sense, because when magick is worked, the Moon's cycle
must be taken into account. When the Moon is full, many people consider
this the strongest, best time to do all forms of magick. The "Full Moon"
influence is said to be happening on the day the Moon is full and the
days before and after. If the Moon is dark, many people prefer not to do
magick at all but to concentrate on darker aspects of themselves and
engage in meditation and things like scrying, which are practices done
by the wise and require lots of experience to do well. As the Moon
becomes a crescent and grows toward being full again (waxing), this is a
good time for catalystic spells; simply put, this is a time to cast
spells that would begin something. These are spells with a "positive"
(not as in "good" but "positive") influence. After the Full Moon, waning
begins and the spells that are cast can be "negative" spells, such as
stopping bad energy, any banishing, getting rid of bad habits, and so
on. I mention how spells coincide with Esbats because so many people
like to use these holidays to work as well as to honor the Goddess.
When you want to honor the Goddess, you should perhaps give Her
offerings or celebrate/honor the female side of nature. You can invoke
the Goddess and read poems and tributes to Her; you can do dances and/or
make music for Her; you can set up a special altar for Her and burn a
candle in the cauldron; you can honor a specifically named Goddess from
mythology and think about that Goddess's attributes; you can do a whole
mess of things. The important point is that you honor the Goddess on Her
turning points as well as honoring the God on His!
For examples of what people do for Esbat rituals, try doing some
research on any mention of "Drawing down the Moon," as that is a popular
activity on the Esbats; in those, a coven gets together and someone
"draws down" the Goddess, in the guise of the Moon, into another woman
(or someone draws the Moon into herself). It is not often done with men,
but it can be done just as a woman can supposedly draw down the Sun. It
is a way of temporarily being "possessed" or inspired by the female
divine, for a purpose of working magick or doing some other activity the
Goddess deems necessary.
A nice solitary activity on the Esbats is to take a deck of Tarot cards
and separate them into the four suits and the Major Arcana, then place
each of the piles at their respective points on the circle or altar
(Pentacles for north, Wands for east, Swords for south, Cups for west,
with the Major in the center). Then ask each element and the God and
Goddess to reveal to you, through picking a card, one bit of advice you
should heed between now and the next month's Moon. Write these down and
interpret them later or interpret them immediately, but try to keep a
record so that you can properly heed the advice.
You may wish to celebrate an Esbat on the New Moon, when no Moon is
visible. In these times, try introspective Dark Goddess rituals, such as
ones where you honor the Crone aspect or attempt divination or astral
projection. This is a nice change from the usual Full Moon rituals, for
use if you have to miss a Full Moon because of your schedule or you just
prefer it, or want to focus on the dark or introspective part of you
for once. It's just as much of a part of life, so don't fear it.