These types of puzzles are known as charades. What you have to do is find two words that are referred to in the first stanza and the second stanza and put them together to form the third word in the third stanza.
Just for example, if my first refers to 'off' and my second refers to 'ice', then my whole will be office.
My first is present - future's past -
A time in which your lot is cast.
My second is my first of space
Defining people's present place.
My whole describes a lack of site -
A place without length, breadth, or height.
A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?
Andrew’s doctor gives him three pills and tells him to take one every half hour. How much time will have passed by the time Andrew’s taken all three pills?
I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?
Jessica is telling her friends this story and asks them to guess if it’s the truth or a lie: “There was a man sitting in a house at night that had no lights on at all. There was no lamp, no candle, and no other source of light. Yet, he sat in the house and read his book happily.†Her friends say she’s lying, but Jessica corrects them and says she’s telling the truth. Jessica’s story is true—but how?
Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.
"Are you twins," ask the headmaster.
"No," replies the boys.