Truth is a noun. True is an adjective. 

Truth is a thing, a piece of information that is right, factual, or real. 

1. The truth will set you free.  Here "truth" is the subject. 
2. All I want is the truth. And here, "truth" is the object. Usually, we use the article the before truth. If you say a truth, it has a slightly different meaning. 
3. It is a truth I have never confessed, This means a fact or another piece of information. This is a figurative expression, so when in doubt, always use the truth. 

True means something that is real, factual, or accurate (you can prove it). You see this a lot on tests. It describes something. 

1. True or False: The sky is blue? (is the statement right or wrong?)
2. That article I read was so true. (the article was honest, it was about real life). 
3. The movie was based on a true story. (it really happened)

Truth is used far more than true. True is often used in set expressions (like the ones above: true or false, so true, and true story). 

However, there is another form of true: Truly. 

1. That mean was truly delicious. (very)*
2. Yours Truly, Greg. (used at the end of a letter to a close friend)
3. Is that so? Truly. (here it means yes). 

Truly is an adverb, so it must be attached to a verb, adjective, or adverb. 

*Note: Truly is used more in writing than in speech. The first example is the most common usage. The third example is the least common. 

True and Truth