There are two answers to this. First, the traditional answer you would get from classical sources like the Sutta Pitaka, which are, at the very least, close to the Buddha's words.
The Buddha's goal was to discover a way to end individual human stress/suffering. His critical analysis of the human condition was heavily bound by personal, empirical experience. This is expressed within the Kalama Sutta, where he advises the Kalamas:
"So, as I said, Kalamas: 'Don't go by reports, by legends, by
traditions, by scripture, by logical conjecture, by inference, by
analogies, by agreement through pondering views, by probability, or by
the thought, "This contemplative is our teacher." When you know for
yourselves that, "These qualities are unskillful; these qualities are
blameworthy; these qualities are criticized by the wise; these
qualities, when adopted & carried out, lead to harm & to suffering" —
then you should abandon them.' Thus was it said. And in reference to
this was it said."
This gives you a basic insight into his method for gaining insight. It does not deny the validity of God, but the Buddha had something to say about faith in concepts that are neither provable, nor verifiable within our experience:
"There are some brahmans & contemplatives with a doctrine & view like
this: 'After death, the self is exclusively happy and free from
disease.' I approached them and asked them, 'Is it true that you have
a doctrine & view like this: "After death, the self is exclusively
happy and free from disease"?' When asked this, they replied, 'Yes.'
So I asked them, 'But do you dwell having known or seen an exclusively
happy world?' When asked this, they said, 'No.' So I asked them, 'But
have you ever been aware of a self exclusively happy for a day or a
night, or for half a day or half a night?' When asked this, they said,
'No.' So I asked them, 'But do you know that "This is the path, this
is the practice for the realization of an exclusively happy world"?'
When asked this, they said, 'No.' So I asked them, 'But have you heard
the voices of devas reborn in an exclusively happy world, saying,
"Practice well, my dears. Practice straightforwardly, my dears, for
the realization of an exclusively happy world, because it was through
such a practice that we ourselves have been reborn in an exclusively
happy world"?' When asked this, they said, 'No.'
"So what do you think, Potthapada — when this is the case, don't the
words of those brahmans & contemplatives turn out to be unconvincing?"
"Yes, lord. When this is the case, the words of those brahmans &
contemplatives turn out to be unconvincing."
"Potthapada, it's as if a man were to say, 'I'm in love with the most
beautiful woman in this country,' and other people were to say to him,
'Well, my good man, this most beautiful woman in this country with
whom you are in love: do you know if she's of the warrior caste, the
priestly caste, the merchant caste, or the laborer caste?' and, when
asked this, he would say, 'No.' Then they would say to him, 'Well
then, do you know her name or clan name? Whether she's tall, short, or
of medium height? Whether she's dark, fair, or ruddy-skinned? Do you
know what village or town or city she's from?' When asked this, he
would say, 'No.' Then they would say to him, 'So you've never known or
seen the woman you're in love with?' When asked this, he would say,
"So what do you think, Potthapada — when this is the case, don't the
words of that man turn out to be unconvincing?"
"In the same way, there are some brahmans & contemplatives with a
doctrine & view like this: 'After death, the self is exclusively happy
and free from disease.'... Don't the words of those brahmans &
contemplatives turn out to be unconvincing?"
This is from the Potthapada Sutta and it addresses exclusively one sides concepts of Self, or Atman. The relationship between the Hindu Atman and the Hindu concept of God (Brahman or Ishvara, depending on whether the deity is impersonal or personal, is complicated, but a close parallel can at the very least be drawn here).
The Buddha's realization was that, within the empirical world*, "every thing that has a beginning, has an end". As such, when you try and find this 'thing' that you look for, this Atman, you 'only' find emptiness. As such, there is no base, no ground on which to build a reistic philosophy (nor for that matter any reason to infer a God, at least not a God that has any Essential properties whatsoever!)
*this is a very important point - the Buddha did not step into metaphysical conjecture, because it was not conducive to the goal of liberation from stress/suffering. In fact, the first Sutta within the Digha Nikaya (a sort of introduction to Buddhism for novices and the curious) denies the validity of all metaphysical speculation. http://www.accesstoinsight.org/tipitaka/dn/dn.01.0.bodh.html and the first Sutta of the Majjhima Nikaya (arguably for the more advanced student) states that 'the root of all things' is not found. https://suttacentral.net/en/mn1
The above realization was key to the First of the Four Noble Truths:
"Now this, monks, is the noble truth of stress: Birth is stressful,
aging is stressful, death is stressful; sorrow, lamentation, pain,
distress, & despair are stressful; association with the unbeloved is
stressful, separation from the loved is stressful, not getting what is
wanted is stressful. In short, the five clinging-aggregates are
If permanence within the empirical world is denied (a property that Atman and God must maintain in some way, in order to be anything more than the mundane impermanence that our experiences reveal to us), then the above follows (like Satre's exsistential dread). From this follows the next Three Truths, which are on the origination of stress/suffering, the cessation of stress/suffering, and the path to end stress/suffering. This is best read from the source! http://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.011.than.html
What is understood is that the Noble Eightfold Path stated in the Fourth Truth, is entirely dependent on the individual. There is not even the slightest removal of power to progress within the path from the individual to any other individual, including any conception of God.
This makes sense because a world view that explicitly states that the ground from which the world manifests is not to be found, explicitly denies that any truth can be gleaned from such a ground (after all, it is not found!).
In denying the validity of reistic world views, the Buddha did not however embrace annihilationism (or nihilism to us). He created a relational philosophy, where things are dependently originated. http://www.accesstoinsight.org/tipitaka/dn/dn.15.0.than.html
(If you like classical logic, here is a nice article on why Essentialism and Nihilism can be treated as the same: https://plus.google.com/+DenisWallez/posts/K9PsvMRQhve )
If you like quantum physics, this is not much different from the relational interpretation of Quantum Mechanics by Rovelli. https://arxiv.org/pdf/quant-ph/9609002v2.pdf Whilst drawing parallels between the scientific method in the late 20th century and the Buddha's world view 2,500 years before that is a complex enterprise, Nagarjuna (the second Buddha to most, and someone who took the Tripitaka as authoritative, took a much more 'Western friendly approach' to this concept of 'dependent co-arising' within his Mulamadhyamakakarika, and you do get comparisons with his reasoning and Rovelli within Western publication: http://philpapers.org/archive/CAPIOQ-2.PDF )
Because the Buddha created a method that denied the validity of a permanent Essence, it ironically gave him the right to say that the power to deliverance from stress/suffering lies in each person's individual power.
With regards to ethics, this is explained in https://suttacentral.net/en/mn8
With regards to the practice of Buddhism, the Maha-Satipatthana Sutta lays out what needs to be done in its entirety: https://suttacentral.net/en/dn22
So to sum up, the Buddha did not place any faith in prayer, mantra, chanting or God. The path is, mostly, walked alone http://www.accesstoinsight.org/tipitaka/kn/snp/snp.1.03.than.html
There are gods within Buddhism, but they are simply beings that through their good karmic actions end up in higher realms (in fact, humans who practice the Noble Eightfold Path diligently can end up in these realms too). But none of them are permanent, and they all still possess the risk of falling into lower realms (including the hells, the animal realms and the human realm), if they act in such a way as to bring bad karma onto themselves. The Buddha neither worshiped nor placed any authority in them.
The second answer is that Buddhism has spread to a very diverse group of people, some of which invoke the power of prayer, mantra, even begin to define Buddha as divine in one way or another. Strictly speaking, this is not Buddhism as the Buddha envisioned.
So! If you place your faith in God and the divine, His power and authority, you will find Buddhism lacking in these respects. But, in that all possible power to act, change and improve, is left within the sphere of influence of the individual, all that is necessary to bring about an end to suffering is already within you. Physical illness the Buddha would have likely advised to leave to those that practice medicine!