If they exist, then how are they connected to the God(s)/Lord Buddha?
I'll answer in two parts-- what sort of looks like a god in Buddhism and which of those are female.
Early Buddhism didn't see gods as important to solving their fundamental problem of ending suffering. Gods were seen as a possible destination for our reincarnation. Gods didn't provide any help to us humans, they were too busy enjoying themselves (devas) or jealously fighting each other (asuras). In Mahayana Buddhism, the devas are not the target of devotionalism, respect and appeal for help, so I'll skip over them. (Except maybe to the extent that they were recast as Bodhisattvas & Buddhas)
Later Buddhism developed the Bodhisattva Path, which was based on the idea that one should strive to become a Buddha. The Bodhisattvas were models of behavior, but rapidly also became devotional targets who would provide various this-worldly benefits, such as defense against snakes.
Also by this time, the Buddha and enlightened people in general were supposed to have extreme long life, the ability to know past lives, to do "astral projection", and so on. As sutras evolved, Buddhas gained more powers until they were indistinguishable from a conventional god from a more familiar religion like devotional Hinduism, Christianity, etc.
There was a lot of controversy about if a woman could reach enlightenment (arahathood) or become a Buddha (full Buddhahood). I think it's not controversial to say that from the time of the historical Buddha the relevant societies were deeply sexist and reluctant to admit that woman could become Buddhas.
Avalokiteśvara was Bodhisattva who once the story arrived in China became a woman (Kwan Yin). Kwan Yin is both a devotional target and a model.
Tara is an important Yidam in the Tantric system. People appeal to Tara both for this-worldly aid and use visualization techniques to imagine themselves as a Tara-- i.e. an enlightened being.
Jan Natier has a good discussion about women in Buddhism, in this paper, although it is is somewhat specific to the Lotus Sutra by the end: https://www.academia.edu/8164216/Gender_and_Hierarchy_in_the_Lotus_S%C5%ABtra
Depending on who you ask, Buddhism does or doesn't have Goddesses. The issue is complex because people define these terms differently, and Buddhism often co-opted the practices of the cultures in which it entered. So some schools of Buddhism may have dieties, others may have Bodhisattvas they venerate, others may claim those Bodhisattvas are de facto dieties and accuse those who claim otherwise of equivocation...
A great example of this is Quan Yin (Guanyin). She is the symbol of compassion and thus she figures very prominently in Buddhist iconography. For instance, at my local Mahayana Temple, there are far more statues of Quan Yin than of The Buddha himself. Quan Yin is not related to The Buddha, she seems to have been a pre-existing Goddess who got co-opted into Mahayana Buddhist belief.
By Depending on who you ask, do you mean the version of Buddhism? And how is Quan Yin related to Lord Buddha?– Dawny33Oct 5, 2015 at 13:12
1@Dawny33 I clarified my answer Oct 5, 2015 at 13:20
Are you a woman? Are you practicing the dharma? Have you set your mind firmly on being re-incarnated into the world of the devas, such that the prospect of a fortunate and privileged rebirth among humans could not possibly entice you?
Then you are a goddess in Buddhism.
Householders, there are these four ways of living together. What four? A wretch lives together with a wretch; a wretch lives together with a female deva (god); a deva (god) lives together with a wretch; a deva (god) lives together with a female deva (god). When both are immoral, miserly and abusive, husband and wife live together as wretches. The husband is immoral, miserly and abusive, but his wife is virtuous, charitable, generous. She is a female deva living with a wretched husband. The husband is virtuous, charitable, generous, but his wife is immoral, miserly and abusive. She is a wretch living with a deva husband. Both husband and wife are endowed with faith, charitable and self-controlled, living their lives righteously, addressing each other with pleasant words. Then many benefits accrue to them and they dwell at ease. Their enemies are saddened when both are the same in virtue. Having practiced the Dhamma here, the same in virtuous behavior and observances, delighting in a deva world, they rejoice, enjoying sensual pleasures. AN 4.53
There're many planes of existence (ref: http://www.accesstoinsight.org/ptf/dhamma/sagga/loka.html). The upper planes are where the devas (gods/godesses) live. Although possessing various supernormal powers, they are still un-enlightened beings like us humans and are still subjected to the cycle of birth and death. Prior to His last rebirth on earth, the Buddha resided on the deva realm called the Tusita Heaven. After attaining enlightenment, the Buddha was no longer a god for He's no longer subjected to the cycle of birth and death.
The question was whether there are Goddesses; and if they exist, then how are they connected to the God(s)/Lord Buddha?– ChrisW ♦Oct 5, 2015 at 15:43
1Let's wait for Dawny33 to decide whether his question has been addressed or not– santa100Oct 5, 2015 at 16:07
1@santa100 I don't think that the question has been addressed by this answer. It has nothing to do with Goddesses, maybe can you explain a bit further?– Dawny33Oct 6, 2015 at 4:28
MatthewMartin's post above pretty much covered it. From a Theravada perspective, gods or goddesses are heavenly beings living in their deva worlds. Other than possessing supernormal powers and endowed with lots of good merits, they're still un-enlightened beings just like us humans.– santa100Oct 7, 2015 at 0:55