Unity in Diversity
(Attrib: The following is based on http://www.quaker.org.uk/quaker-beliefs)
Quakers do not share a fixed set of beliefs.
Our unity is based on a shared practice of worship, not on our beliefs all being the same. There is no need to be in unity with Quakers on every issue in order to be part of our meetings.
Many people have a personal understanding of God; often this is based on Christian teachings, or on other religious traditions. Other people are aware of or seek a spiritual environment but would not define it further. Quakers are no different!
There is a great diversity within the Quakers on conceptions of God, and we use different kinds of language to describe religious experience. Some Quakers have a conception of God which is similar to that of orthodox Christians, and would use similar language. Others are happy to use God-centred language, but would conceive of God in very different terms to the traditional Christian trinity. Some describe themselves as agnostics, or nontheists, and describe their experiences in ways that avoid the use of the word God entirely.
Quaker faith is built on experience, and Quakers would generally hold that it is the spiritual experience which is central to Quaker worship, and not the use of a particular form of words (whether that be "God" or anything else).
(Attrib: From 'Rooted in Christianity, Open to New Light', Chapter 8: 'Naming our Common Ground' by Alex Wildwood)
In the light of the range of faith positions now existing within the Society, it is quite a challenge to attempt to define the implicit beliefs of Quakerism, but what I can offer here is my personal view. I would say they boil down to the following:
As Quakers we believe that in the silence we may hear "the still small voice of God". We believe that through this we will be led to compassionate action in the world; Friends are not a church focused on personal salvation or enlightenment, but on redemption of the world from suffering, injustice and oppression. We believe that the 'will of God', understood as the right way forward, the truth of a situation, will be revealed in the stillness of expectant waiting together.
We believe "that of God" to be present in all people and beings and that "obedience to God" (listening for the truth, perceiving reality directly) leads us to live according to our testimonies, which is a way of life where truth, equality, simplicity and peace become the touchstones of personal lives and all our dealings with others - from intimate relationships to the global arena. these beliefs may be implicit in Quaker practice rather than stated explicitly, but I would say that it is on all these beliefs that Quakerism is founded.
Watford Quaker Meeting in London have produced a series of videos of personal reflections on aspects of Quaker faith.