Since this is a wide-open question, the best approach is to summarize the teachings the of Buddha:
(1) Everything is connected;
(2) Nothing lasts;
(3) You are not alone.
These first three are really just a restatement of the traditional Three Marks of Existence: non-self, impermanence, and suffering. The fact that we all suffer means we are all in the same boat, and that's what allows us to feel compassion.
(4) Life is full of suffering
(5) Suffering exists because of our desires and aversions.
(6) There is a state of mind in which suffering ends (enlightenment).
(7) There is a path to attain this state; That path is called the Eight Fold Path.
Items 4 - 7 are the Four Noble Truths.
(8) Bodichitta (Loving- Kindness / Compassion) is the first step to enlightenment (and to solving the world's problems)
(9) The 5 Precepts concisely describe a moral life
The 5 precepts are:
(1) not to take the life of any sentient being,
(2) not to take anything not freely given,
(3) to abstain from sexual misconduct and sensual overindulgence,
(4) to refrain from untrue speech, and
(5) to avoid intoxication, that is, losing mindfulness.
(10) Mindfulness of thoughts and actions are the key to wisdom and therefore
to the path of enlightenment.