Bueno, -a; Buen; Bien
The word "bueno, -a" is usually used as an adjective. It's a modifier and is used to denote the quality (i.e. the goodness) of the thing being named. Example, "la comida está buena" (the food is good); "es bueno leer" (it's good to read); "son buenos chicos" (they're good guys).
The word "buen" is an adjective too, but it's also an apocope. What is an apocope? Well, it's the loss of one or more sounds from the end of a word; especially, the loss of an unstressed vowel. With the word apocope from "bueno" to "buen", it only happens before a masculine singular noun. Example: "este libro es bueno" (this book is good); but then, "es un buen libro" (it's a good book). Or another example: "el café está bueno" (the coffee is good); but then "el buen café me gusta" (I like good coffee).
The word "bien" is usually used as an adverb. As such, it modifies a verb, an adjective, another adverb, a preposition, a phrase, a clause, or a sentence, expressing some relation of manner or quality, place, time, degree, number, cause, opposition, affirmation, or denial. So you can see, there are lots of different usages for it, even when it's just used as an adverb. Before an adjective or adverb, it can have the meaning of "muy". Example: "es bien tarde" = "es muy tarde" (it's very late); "la comida está bien rica" = "la comida está muy rica" (the food is very delicious). It can also mean "sano" (healthy) or "de buena salud" (in good health). Example: "ella se siente bien" (she feels well); "estoy bien" (I am well). It can also mean "sin inconveniente" (without an inconvinience). Example: "bien puedes hacerlo" (you can easily do it); "...como bien sabes" (...as you well know). With some participles, it works almost as a prefix. Example: "está bien dicho" (it's well said); "bien hecho" (well done).
Remember, these are some of the possible meanings for these words. Surely we can find other cases as well to talk about. I hope this helps to clear up the confusion between them.
