Modern paganism incorporates many new and old traditions, and has formed itself into modern collective groups, and are religions although most do not associate themselves with modern othrothdox belief systems. Each is unique and has its own viewpoints and traditions, but each are clearly what can be called Pagan from their basic formula of thought. Generally, modern pagan traditions fall into one of the following four larger categorized groups.
Classical Paganism - This is the practice of pagan traditions that usually pre-date Christianity, and are still practiced to the modern day. This includes eastern, western, shamanism and aboriginal traditions. The practitioners try their best to follow the rituals and methods as they were originally practiced and do not incorporate ideas from other traditions, trying to achieve the purest similarity to how the original beliefs practiced their religion. These belief generally include the ideas of pantheism, ritualism, polytheism and animism. This includes but is not limited to Voodoo, Wicca, Odinism, Shinto, Hinduism, Taoism, and many other lesser proto-religious forms.
Neopaganism / New Age - This is the practice of classical pagan traditions, but also includes modern religious rituals and ideology often based on the individual and their background. The main difference between neopagans and those who practice classical paganism is the incorporation of modern religious dogma and rituals ( such as monotheistic ideas and other non-pagan beliefs ) and the intermixing of various rituals and traditions from other pagan beliefs without discrimination. Neopaganism and New Age have this similarity in common, and therefore are often put together for generalized explanation of their belief systems. Also they are both products of the post-cold war era for the most part.
Technopaganism - This is a relatively new kind of twist on the outlooks of what are traditionally called paganism. In essence the key idea is that modern technology, devices, computers and artifacts of the post-industrial world can be used as sacred or magical tools, just as the challis or athame have been in classical and neopaganism. Also technopaganism sees modern musical styles, synthesized writing, digital arts, and even computer code as sacred music, text, and basis for what older religions would have used hymns and scripture to supplicate. This is a wide subject and would be unfair to discuss without further discourse.
Discordanism / Nihilism - This is the incorporation of the existential idea that morality does not truly exist, and that any such ideas in a dogmatic system are artificially contrived. So is the discordianistic idealism, that chaos, discord, and dissension are more desirable qualities in a true human being, than are harmony, faith, and order as proposed by religions in former centuries. Also the scientific and skeptical model of reality is upheld. Therefore true knowledge is not possible, and that despite what we wish to believe, reality does not inherently exist as such. Nihilism is a vein of many subcultural beliefs. Most profoundly in the ideas of anarchism, ecological movements, and modern Satanism.
These four can be elaborated on more in depth, but for basic understanding of what it is to be a modern pagan, these are the basic classifications that you will find most fit. As with any religions or dogmas there are widely accepted versions and more secular ones depending on who is practicing the rituals. As time passes, there are likely to be more expansions on these themes, for modern pagan beliefs are an ever evolving art unto themselves.
"Ordinary mortality is for ordinary people." - Aleister Crowley