Let's say that Islam, Christianity, Judaism and Buddhism are like tiramisù: there's a recipe, some main ingredients that are always the same and make up most of the recipe, and some variations on the recipe. There can be a god, then a messiah or a prophet, sacred texts, rules and rituals, variations on the main theme ("denominations"), and every person follows that religion or its denominations. Using the same metaphor, talking about Hinduism is like talking about Italian cuisine: there's the basic idea to eat to stay alive and healthy, and then recipes and ingredients vary according to region, province, district, village, down to the single individual. The English word Hinduism itself is an umbrella term, first used in the early 1800s, to describe a very complex ecosystem of beliefs.
Hinduism has been defined as a religion, a religious tradition, a set of religious beliefs, and a way of life. In India, the term dharma is preferred, which is broader than the Western term "religion".
Hinduism's varied history overlaps or coincides with the development of religion in India since the Iron Age (1500 to 600 BC), with some of its traditions tracing back to prehistoric religions such as those of the Bronze Age (3000-2600 BC).


Still, not all of these themes are found among the various systems of Hindu beliefs.

Karma: an action and its consequences.
Samsara: the cycle of death and rebirth.
The four purusarthas (goals of human life):
Dharma: duties, rights, laws, conduct, virtues, right way of living. Behaviour in accord with the order and custom that make life and the universe possible.
Artha: career, skills, health, wealth, prosperity. The means needed for a fulfilling life.
Kama: desire, passion, pleasure. Enjoyment of art, beauty, life, affection and love, with or without sexual connotations.
Moksha: liberation from the passions and the cycle of death and rebirth.

How these are linked is pretty intuitive. You want to achieve the moksha and stop the painful samsara, and the path to do so goes through dharma, artha and kama, while inevitably having to deal with karma.

It's also apparent that artha and kama are in contradiction with moksha. Historical Indian scholars recognized and debated this inherent tension and they proposed nishkama karma as a possible solution: selfless or desireless action, an action performed without any expectation of results.

I read more about nishkama karma and it sounds like a far-fetched, sugar-coated version of "shut up and work". So I read more about the purusarthas. Older scriptures (Samhitas, Brahmanas, Aranyakas) refer to artha, kama and dharma as trivarga, three categories of "possible pursuits". The concept of moksha appears in a later scripture (Upanishads). The four appear together for the first time as "goals" in even later scriptures (Dharmasastras, Ramayana, Mahabharata). Rajendra Prasad (2008) states that the division between trivarga and moksha was originally intended to highlight the difference of context between the social (trivarga) and personal (moksha) spheres. A society necessarily includes artha and kama, but one can opt for sannyasa (life of renunciation), which focuses on moksha. In both cases, dharma prevents chaos.


Concept of God:

Polytheistic: there are many gods.
Pantheistic: the universe is God.
Panentheistic: God includes the universe but goes beyond.
Pandeistic: God became the universe.
Henotheistic: there's one main god and other minor gods.
Monotheistic: there is one god.
Monistic: the universe comes from one origin or one substance only.
Agnostic: the existence of God is unknowable.
Atheistic: there is no God.
Humanist: reliance on science rather than God.

Texts:

Vedas: mantras, benedictions, rituals, ceremonies, sacrifices, meditation, philosophy and spiritual knowledge. The Vedas are thought to be revelations heard by ancient sages after intense meditation.

Upanishads: meditation, philosophy, consciousness and ontological knowledge. They document the transition from the archaic ritualism of the Vedas into new religious ideas and institutions.

Puranas: cosmogony, cosmology, genealogies of gods, goddesses, kings, heroes, sages and demigods, folk tales, pilgrimages, temples, medicine, astronomy, grammar, mineralogy, humour, love stories, theology and philosophy. They don't have the same authority of a scripture but they shaped Hinduism more than the Vedas.

Mahabharata (incl. Bhagavad Gita): events and aftermath of the Kurukshetra War, a war of succession between two groups of cousins, the Kauravas and the Pandavas. It also contains philosophical and devotional material, such as a discussion of the four purusarthas. It has been said that if there is any one text that comes near to embodying the totality of Hindu thought, it is the Bhagavad Gita. The latter is set in a narrative framework of dialogue between the Pandava prince Arjuna and his charioteer Krishna, eighth avatar of Vishnu.

Ramayana: the life of Rama, seventh avatar of Vishnu and prince of Ayodhya in the kingdom of Kosala. Narratives of past events interspersed with teachings on the goals of human life.

Agamas: cosmology, epistemology, philosophical doctrines, precepts on meditation, four kinds of Yoga, mantras, temple construction, deity worship and ways to attain sixfold desires. The Shakta Agamas are commonly known as Tantras. They are imbued with reverence for the feminine, which embodies creation and, unified with the male principle, the Absolute.

Gods:

The main deities based on the most popular currents:

Vishnu (Vaishnavism): supreme god who creates, protects and transforms the universe but known as "the Preserver" within the trinity with Brahma and Shiva, the Trimurti. The latter represents the three fundamental forces through which the universe is created (Brahma), preserved (Vishnu) and destroyed (Shiva) in cyclic succession.

Shiva (Shaivism): supreme god who creates, protects and transforms the universe but known as "the Destroyer" within the Trimurti (see Vishnu).

Devi (Shaktism): goddess, wife of Shiva. The two are considered complementary principles to each other. She is "activated Time", while he is "non-activated Eternity". In the Tantras, Shiva says: "O Goddess, I am the body and you are the conscious spirit within the body".

Ganesha, Shiva, Devi/Shakti, Vishnu, Surya (Smartism): all five treated as equal. Ganesha is one of the best-known and most worshipped gods in the Hindu pantheon: remover of obstacles, bringer of good luck, patron of arts and sciences, deity of intellect and wisdom. Surya is a solar deity.

Other popular gods:

Krishna: eighth avatar of Vishnu or Supreme God in his own right.
Brahma: "the Creator" in the Trimurti (see Vishnu), yet famously neglected.
Kali: goddess of time, death, violence, sexuality, female power and motherly love.
Rama: seventh avatar of Vishnu or Supreme God in his own right.

Gods can be one to hundreds, and they can be known under different names (epithets and incarnations/avatars). According to a common misconception, Hinduism would have 33 million or 330 million gods. The mistake is due to the wrong translation of "33 koti" in the Vedas, as koti means both "types" and "10 million".

Common religious practices:

Devotion (bhakti): spiritual love that engages both emotion and intellection.
Worship (puja): offering light, flowers, food or water.
Sacrificial rites (yajna): surrendering animals, food, water or goods through fire.
Meditation (dhyana): a step of Yoga to find one's relationship with Reality and God.
Yoga: controlling body and mind to find one's relationship with Reality and God.

Tantra ("technique") is an esoteric yogic tradition that involves mantras, breath control and body manipulation.

Schools of philosophy:

Sankhya: the universe is composed of two realities: consciousness and nature. A living being is a state in which consciousness is bonded to nature through a combination of senses, feelings, activity and mind. The bondage is due to wrong knowledge. Moksha can be attained through insight.

Yoga: like Sankhya, but moksha can be attained through insight and physical discipline.

Nyaya: human suffering results from mistakes produced by activity under wrong knowledge. Moksha can be attained by understanding the true nature of soul, Self and Reality. Anything that exists is in principle humanly knowable.

Vaisheshika: knowledge and moksha can be attained through a complete understanding of the world of experience (the physical universe).

Mimamsa: humans seek happiness, which is the result of ethical actions (dharma). The Vedic sentences contain such actions, so it is important to properly interpret and understand the Vedas.

Vedanta: explanations and interpretations of the Vedas. Investigation of Self, Ultimate Reality, samsara and moksha.  

Note: Yoga and Tantra appear in different categories, which might be confusing. Yoga is first of all a philosophy or religion, which includes several practices, which can be carried out separately from the philosophy and from each other. The Tantras are first of all texts (also called Shakta Agamas), which include techniques (mantras, spells, symbols) to be used in many contexts: theology, temple building, religious practices and sex.