Buddhism may appear in different forms, varying from one observation to another: from one Buddhist school to another, from country to country, from culture to culture, and among different self-claimed Buddhist groups and subgroups. Despite all changes in time and space, Buddhism's core or true nature remains the same, and it should be respected and preserved as it is. Buddhist followers should discriminate true Buddhist teachings and practice from distorted forms of Buddhism.
Buddhism is a science. One of its goals is to understand the true nature of all events and phenomena (the world inside and outside us). Buddhism emphasizes logic, intellectual arguments, empirical or evidence-based experiments (what the individual Buddhist practitioner actually experiences), critical analysis and thinking. Buddhism is not based on blind faith, but genuine Buddhists do have a strong belief in the capability of all beings to attain Buddhahood (the Buddha Nature which is inherent in every being) through the individual's strong right volition, effort, wisdom and practice. A Buddhist is fundamentally an atheist.
Buddhism is a philosophy. Buddhist dhamma teachings expound a way to view humanity and the worlds/universes, and a way to live and function in the human world. Buddhist philosophy emphasizes nonviolence, compassion, tolerance, courage, equanimity...and, above all, wisdom. Wisdom and intellectual capacity dominates Buddhist life philosophy in the sense that wisdom must guide all Buddhists' thoughts and actions.
Buddhism is practice. Buddhism is not for theoretical or scholastic academia discussions. Buddhism is for application and experience for the better of the individual and all sentient worlds at large. Buddhist practice is the reason why the Buddha appeared and taught the Dhamma, the path that leads to the individual's ultimate liberation from all sufferings and from Samsara (the cycle of birth and death). Unless a Buddhist follower practices the methods which the Buddha taught, all Buddhist teachings (from Tripitakas) would lead that person to nowhere, that is, s/he would not benefit from the Buddha's teachings. On the other hand, if practicing rigorously under the guidance of a genuine guru (a genuine Buddhist monk/nun master), the individual can gauge/experience his/her progress, see the results of the practice (the application of Buddhist dhamma) in his/her life as manifested through his/her own body, words and thoughts. There must be a huge inner or spiritual transformation after a while, depending on many internal and external factors. Although there are many levels of liberation, just as there are many levels of ignorance, the genuine Buddhist practitioner's ultimate goal must be to liberate oneself from the cycle of birth and death. After that personal attainment, it is up to the person to choose how to help others to attain the same goal as s/he has reached.
The practice includes disciplines (precepts at various levels), meditation, and wisdom development. The Buddhist follower first has to master (learn, read and listen to) the Dhamma teachings (Tripitaka). Second, s/he must think over and over about, or mull over, these teachings, while observing the teachings in action in daily happenings within him-/herself and in the outside world. Third, the person needs to practice meditation (samatha and vipassana). Every practitioner is free to follow the method that fits him-/herself the best, for different practitioners have different levels of karma and spiritual development. Without precepts or disciplines, it would be very difficult for a person to go further. Therefore, precepts or disciplines must be the basis of all practice.
It is up to the individual follower to view Buddhism as a religion or not. Rituals and any forms of Buddhist practice are only forms, and should be viewed as such only. The method leading to the goal is not the ultimate goal. Therefore, do not mistake the finger that points to the moon for the moon itself. Throw away the raft you have used once you have reached the other shore of the Samsara river. Do not carry the raft along all the way, when it is no longer useful.
Source:
Multiple sources, mainly based on the 14th Dalai Lama's teachings.