You can use the word "true" in at least three ways. Something can be propositionally true, ontologically true, or ethically true. These three are related and there's much overlap between them.
Propositional truth deals with the correspondence of language to reality. To the extent that language accurately conveys reality it is true. Only propositional sentences can be "true" in this sense. An example would be a statement like: "God created the heavens and the earth." That statement is either propositionally true or false. Non propositional statements such as "shut the front door" cannot be true or false. "God created the heavens and the earth" is propositionally true.
Ontological truth deals with the purity or quality of a thing. True gold, as opposed to fool's gold, is a substance that is purely and truly gold. HBO's popular "True Detective" tells a story of people who are truly, at the core of their beings, detectives. Yahweh is the true and living God.
Ethical truth deals with moral virtue. A person can be "true". This might mean that they're trustworthy, faithful, or not a hypocrite. Yahweh is true to his word and faithful, worthy of our trust.
2. How can I discover and understand truth, whatever that may be?
It depends on what kind of truth you're going for. You can discover propositional truth by examining statements and their relationship with reality.
You can discover ontological truth by first hand experience with the thing in question. How do you know if something is truly gold? You've got to conduct the proper tests.
You can discover ethical truth by getting to know a person and building a relationship with them.
3. Why should I care? In other words, why should I care about what truth is and how to find it?
Also depends on what kind of truth you're looking for.
Propositional truth is usually good to have because it makes the world less confusing.
Ontological truth is good to have if you care about having, say, true gold instead of fools gold.
Ethical truth is good to have if you care about knowing who you can depend on and who you can't.
In short, truth always seems to be useful for living a long and prosperous life.