Here are some examples:
Adverb:
* "I simply don't understand." (modifies the verb "understand")
* "It's simply not true." (modifies the adjective "true")
Adjective:
* "The simple truth is, I'm lost." (describes the noun "truth")
* "It's a simple matter of time." (describes the noun "matter")
To determine the part of speech, consider how the word is being used in the sentence.