One way to understand Buddhism, is to understand how the Buddha frames happiness and suffering and what he was trying to achieve.
Wordly Happiness & Suffering
First, the Buddha did not denied that we experience pleasure:
“Ānanda, there are these five cords of sensual pleasure. What five? Forms cognizable by the eye that are desirable, lovely, agreeable, pleasing, sensually enticing, tantalizing. Sounds cognizable by the ear … Odours cognizable by the nose … Tastes cognizable by the tongue … Tactile objects cognizable by the body that are desirable, lovely, agreeable, pleasing, sensually enticing, tantalizing. These are the five cords of sensual pleasure. The pleasure and joy that arise in dependence on these five cords of sensual pleasure: this is called sensual pleasure.
“Though some may say, ‘This is the supreme pleasure and joy that beings experience,’ I would not concede this to them. Why is that? Because there is another kind of happiness more excellent and sublime than that happiness."
-- SN 36.19
One problem with the pleasure/happiness that we experience normally, (through our senses, thoughts, emotions) is that they are impermanent. In this sense, they are only temporary shelters in our lives. A second problem is that they seem unable to absolutely satisfy us, in the greatest sense. For example, eating may satisfy hunger at a certain moment, but does not satisfy every single necessity or desire at that same moment.
In the pāli scriptures, the term that describes the characteristic of being impermanent is anicca. And the term to describe the unsatisfactoriness of things is dukkha. With that said, the Buddha declared:
"All sankhara are dukkha."
"All sankhara are anicca."
-- AN 3.136
sankhara is usually translated as "phenomena", "formations", "fabrications" or "preparations". It refer to the "things", all these "fluxes" that are experienced, touched, heard, smelled, seen, felt, thought, etc. Everything that comes to be with conditions as basis.
At this moment, it's relevant to point out that dhukkha can also mean pain or suffering as well. So, that explains why some people came to conclude that the Buddha said that everything (or life) is suffering, which is problematic, as it should be clear now.
What he said, then, is that all these worldly experiences we go through are unsatisfactory in it's ultimate sense. And even if they may be temporarily pleasing at the present, they always carry the danger of suffering in the future. The Buddha also said:
“Then, bhikkhus, it occurred to me: ‘The pleasure and joy that arise in dependence on form: this is the gratification in form. That form is impermanent, suffering, and subject to change: this is the danger in form. [repeats for all aggregates of our individuality]"
-- SN 22.26
That is, by evaluating all experienced based on our sensory faculties, he established the pleasure that arise with them as condition (the gratification). And due to it's characteristics of being impermanent, he observed it carries a danger for suffering.
That sums up the first noble truth: "this is dukkha".
“Bhikkhus, there are these five situations that are unobtainable by an ascetic or a brahmin, by a deva, Māra, or Brahmā, or by anyone in the world. What five? (1) ‘May what is subject to old age not grow old!’ ... ‘May what is subject to illness not fall ill!’ [...] (3) ‘May what is subject to death not die!’ [...] (4) ‘May what is subject to destruction not be destroyed!’ [...] (5) ‘May what is subject to loss not be lost!’."
-- AN 5.48
While most people are fine with all that situation of living with pleasures and sufferings, others feel enslaved by this existential situation they find themselves in. These people came to conclude that no matter what happiness they may find in the world, they know deep inside that such happiness has an expiration date -- and suffering is around the corner. The Buddha was in this later category.
The problem the Buddha set out to solve was: is there the ultimate happiness? and how to achieve it? By ultimate happiness, it's meant something that has no trace of unsatisfactoriness. And also, something that is not impermanent. Because it doesn't change, and because there's nothing else to desire, this is then the ultimate peace, where there's no danger whatsoever of suffering. It's impossible, then, to conceive any happiness greater than that, for this would denounce it's unsatisfactoriness.
In Buddhism, this is called Nirvana, the end of dukkha without reminder. And the third noble truth is a declaration by the Buddha that Nirvana can be attained: "This is the cessation of dukkha".
Because all the "worldly experiences" are conditioned, impermanent, subject to change and to vanish, the Buddha halted any of his attempt to find the ultimate happiness on these things.
Bhikkhus, it is impossible that a bhikkhu who considers nibbāna to be suffering will possess a conviction in conformity [with the teaching]. [...] [But] it is possible that a bhikkhu who considers nibbāna to be hapiness will possess a conviction in conformity [with the teaching]."
-- AN 6.101
What makes our situation more dramatic is the idea of the cycle of births. While some people don't believe in life after death, the tradition understands the Buddha declaring that after the death of this life there's another (and on it goes), seemingly with no external force that will make it stop.
Some may see this as an endless opportunity for entertainment and living all sorts of interesting things. But others see it as a burden. Here, we go around experiencing things that come to an end, and then experiencing other things, with no pause. Sometimes they please us, sometimes they cause suffering. Things that were something become otherwise, continually. Everything we hold with our hands vanish -- and soon, our hands also vanish.
The Buddha concluded that this "never ending wandering" has a cause: our thirst (tanha), our desires, specially the desires based on the sense faculties. By desiring, we keep experimenting, and these experiences have the nature of changing, the nature of being unable to satisfy us, and the nature of cause suffering.
This thirst, then, is a root of our suffering, the second noble truth: "this is the origin of dukkha."
“Long have you (repeatedly) experienced the death of a father… the death of a brother… the death of a sister… the death of a son… the death of a daughter… loss with regard to relatives… loss with regard to wealth… loss with regard to disease. The tears you have shed over loss with regard to disease while transmigrating & wandering this long, long time—crying & weeping from being joined with what is displeasing, being separated from what is pleasing — are greater than the water in the four great oceans.
“Why is that? From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. Long have you thus experienced stress, experienced pain, experienced loss, swelling the cemeteries — enough to become disenchanted with all fabricated things, enough to become dispassionate, enough to be released.”
-- SN 15.13
Thus, the Buddha taught a progressive training where gross and worldly pleasures are gradually abandoned in favor of more sublime and beneficial pleasures.
If by renouncing a lesser happiness one may realize a greater happiness, let the wise man renounce the lesser, having regard for the greater.
-- Dhp 290
This training is the noble eightfold path, the fourth noble truth: "This is the path that leads to the cessation of dukkha."
The Buddha said this path is "good in the beginning, good in the middle, and good in the end". It promotes happiness in this very life, happiness in the after-life, and if taken to it's last consequences, to Nirvana.
It's not known exactly what happens to someone who attained Nirvana after death. When questioned about it, the Buddha did not answer. He denied that after death, an Arahant or Buddha is annihilated. He also denied that he reborns. Finally, he asked that those things that he left undeclared to be remembered as undeclared by him.
But, from what we know he has said, Nirvana is the cessation of dukkha and the end of suffering. We also know that it is said to be, indeed, happiness. So Buddhism is not depressive. It is, in fact, positive. It promotes knowledge about the nature of suffering and happiness and how to cultivate the latter. And to those "tired of the rollercoaster", it affirms there's indeed a secure shelter out of it and shows the path that leads to it.