“Simply” is an adverb; it modifies verbs, adjectives, etc. “Simple” is an adjective; it modifies nouns. In normal speech, the signifier “simply” is used to mean “without excess” or “without complication” and is a way for the speaker to indicate that the speech or act referred to is without guile, without any complicated subtext: “This dessert is simply delicious” would mean that the speaker is giving the dessert his/her unqualified approval, without any other descriptors (sweet, tart, crispy, etc.). “Simple” as an adjective refers to the state or condition of an object or act: “It comes with simple directions.” The word “simple” also is sometimes used to refer to a person’s mental capacity, as a criticism: “Don’t take him seriously; he is simple.” In Shakespeare’s Sonnet 138, the line, “Simply I credit her false speaking tongue:” means that the speaker is taking her utterance at face value, naively (some “translations use ‘foolishly’), without assigning any duplicitous motives to his love.
"Simple" and "simply" are different parts of speech. They are related - kind of like members of a family - but can't quite do the same jobs.
"Simple" is an adjective. That means it describes a noun (a person, place, thing or idea). Here is an example phrase:
"A simple task" - The noun is task, and simple describes what kind of task.
Another meaning of "simple" is "ignorant". It is sometimes to describe someone with low IQ, usually in older books or papers. The word is not commonly used in this way anymore. An example phrase for this meaning of "simple" would be "a simple man" - a man who is ignorant.
"Simply" is an adverb. It modifies a verb (an action word) and describes how something is done. Other examples of adverbs are quickly, anxiously, happily and earnestly. Adverbs frequently end with -ly, which is a clue if you are trying to determine what part of speech a word is.
Here are some examples of the adverb simply used in sentences:
"She decorates her house simply." - "Decorates" is a verb, and "simply" describes how she decorates.
"He simply said no." - "Said" is a verb, and "simply" describes how he said no.
If you get stuck on the difference between similar words, you can check the dictionary. It will tell you what part of speech each word is, which should give you a clue as to how they are different and how to use them correctly.