What are some of Buddhism's Central Ideas?

Answer 1

Central ideas associated with Buddhist practice and Western psychotherapy also have vastly different meanings in East and West, differences that could produce complications if unattended to or precipitate counter-productive responses and actions in the lives of Westerners engaged in Buddhist meditation.
Eastern teachers develop skills that sustain the observation and abandonment of anger, while Western psychotherapists counsel the acceptance, and even encourage the expression of anger.

Easterners attempt to cultivate an impassioned perspective on life, while Westerners authorize the passionate engagement with life.

Buddhist meditation emphasizes non-attachment, while Western psychology talks in dualistic terms of either detachment or attachment.

In the case of anger, for example, there is clarification needed about how it functions in East and West. In the former, anger is to be observed and abandoned in light of the goal of abstaining from harmful intent and harmful action.
Further, given the tendency of Easterners to respond somatically rather than emotionally, anger is to be acknowledged, but not allowed to fester and develop into hate (which constitutes the motivating intention to inflict harm on others).

The basic context here is informed by that of karmic retribution: anger leads to harm which produces, in turn, negative karma, precisely that which propels the pain and suffering of this world.

In the West, by contrast, we are dealing often with the repression of feelings, buried painfully deep within the self but on the verge of bursting forth.

Similarly, with regard to nonattachment versus attachment, Buddhist views should be understood as a via media between fixated attachment on the one side or disengaged detachment on the other, even while Western psychology can distinguish a "healthy secure attachment" characterized by loving and mutual relationship from either "avoidant attachment," which disengages because of past hurts, or "ambivalent attachment," which clings because of needs unmet by an unresponsive other.

With regard to the apparent impasse between the Buddhist no-self and the Western individualized ego, Buddhist mindfulness meditation allows Westerners to see the interdependence of all things which in turn tempers their individualistic tendencies and individualizing habits, while Western psychotherapy provides for strategies to engage the distinctive challenges of late modern life even as it clarifies the limits of what meditation can accomplish.

Answer 2

The central ideas is Buddhism are the Four Noble Truths; the Noble Eightfold Path and the 10 Paramita. (or culmination of practices) I have listed these below, however it will take more then a brief Q & A session to understand them. I have included links below that should help you understand them a little better should you decide you would like more information.

The primarily guiding principle of Buddhist practice is the Middle Way. The Middle Way the practice of non-extremism, meaning that you do not deprive yourself of anything yet you do not flourish in excess either. In other words Balance. In Ch'an (Zen) Buddhism this can be symbolized through the In & Yang symbol, although this symbol predates Buddhism in China it was adapted into the Buddhist philosophy as were many of the Taoist principals. Even today, many Ch'an and Zen students read the Taoist text, "Tao Ta Ching" because it's basic principals mirror many of the Buddhist principals.

One important aspect of Buddhism to note is that there are many different schools of Buddhism that focuses on different aspects of the Buddha's Teachings. None of these schools in more correct or better then any other. It depends entirely on the practitioner. What is useful to one student my not work with another and what doesn’t work for one may be helpful to others. If you wish to learn more, ask about different schools of Buddhism or look them up for yourself. Personally, I follow the Ch'an and Seon (Chinese and Korean Zen) schools of thought. That is not to say I think these are better schools, just better for me. You may prefer the Japanese Zen or the Chinese Pure Land or one of the schools of Tibetan Buddhism. Only you can decide that for yourself. Whatever school you choose, if you schools to study the Buddhas teachings, the core principals are the same.

DETAILS:
The Four Noble Truths:
1) All life is suffering.
2) Craving and desire lead to Suffering.
3) There is a way to end craving and desires and thus suffering.
4) The way to end suffering is the Noble Eightfold Path.

The Noble Eightfold Path:
1) Right View - Realizing the Four Noble Truths.
2) Right Intention - Commitment to mental and Ethical growth in moderation.
3) Right Speech - One speaks in a non hurtful, not exaggerated, truthful way.
4) Right Action - Wholesome action, avoiding action that would hurt others.
5) Right Livelihood - Ones job does not harm in any way oneself or others; directly or indirectly.
6) Right Effort - One makes an effort to improve.
7) Right Mindfulness - Mental ability to see things for what they are with clear consciousness.
8) Right Concentration - State where one reaches enlightenment and the ego has disappeared

The 10 Paramita (culmination of practice):
1) Dana paramita: generosity, giving of oneself
2) Sila paramita : virtue, morality, proper conduct
3) Kshanti paramita : patience, tolerance, forbearance, acceptance, endurance
4) Virya paramita : energy, diligence, vigor, effort
5) Dhyana paramita : one-pointed concentration, contemplation
6) Prajna paramita : wisdom, insight
7) Upaya paramita: skillful means
8) Pranidhana paramita: vow, resolution, aspiration, determination
9) Bala paramita: spiritual power
10) Jnana paramita: knowledge

(In short, the Buddha teaches that nothing last forever and everything is impermanent so worrying about material things is a waste of time especially when all it can cause is suffering. To end suffering you must think, speak and behave with compassion to all things.)

I hope this helps!