***** NOT A TEACHER *****
Hello, Mr. Corter:
In my OPINION, maybe we can parse your sentence like this:
I = subject.
take = verb.
things = object.
a step = a noun that is functioning as an adverb (SOME books call it an "adverbial objective.") It modifies the verb "take." That is, "I take things to the extent of a step at a time."
at a time = prepositional phrase that modifes "a step."
Please study this example from my book: "The package arrived the day before yesterday."
The book parses it as:
The package = subject.
arrived = verb.
the day = a noun that is functioning as an adverb, modifying the verb "arrived." [My note: The package arrived to the extent of the day before yesterday.]
before yesterday = prepositional phrase that modifies " the day."
*****
"To take things a [one] step at a time." In my OPINION, to do something in an orderly, planned manner.
If I want to be the president:
1. I get a good education.
2. I get elected to be the leader of my city.
3. I then get elected to be the leader of my state.
4. I then get elected to the parliament of my country.
5. I then get an important job helping the president.
6. Then I become the vice-president.
7. Finally I become the president!
James
That book: Pence and Emery, A Grammar of Present-Day English (1963).