Kanji help, please
 

Through research I have found 幸福 to translate to "happiness."
However, I was wondering if each symbol by itself has a specific meaning? For example, does each one represent a various form of "happy" that when placed together form the above meaning? Thanks for any help.

First, I hope you are aware that 幸福 is not originally a Japanese word but it was borrowed from Chinese. In Chinese, kanji compound words do NOT always work like math. In fact, many two-kanji words consist of two kanji with very similar meanings. 幸福 belongs in this group. If you do not do this, too many Chinese words will be single-syllable long, making it extremely difficult to use for aural communication.

The dictionary meanings of each kanji are as follows:
幸 fortunate, lucky
福 good fortune, happiness

Well that answers a long-standing question I've had with words like this. Thanks!

Wow, what a coincidence! We also borrowed exactly the same word into Vietnamese :D In case anyone needs to know, the word is "hạnh phúc", which has the latter half sounding very similar to its Japanese counterpart (福). I think this is one of the cases in which the borrowed words has the same connotation in different languages, unlike with the words whose meaning changed over time.