"Turn the trick" is a double entendre, meaning it has two meanings. The surface meaning is that Blanche realizes she is aging. This makes it more difficult for her to "turn the trick" of presenting herself as delicate, alluring, and charming to men. It is important to her to attract male help because she believes she is too soft, weak, and dependent to make it on her own.

The alternative meaning, given what Stanley finds out near the end of the play, is that Blanche is getting too old to "turn a trick" as a prostitute. Turning a trick in this context means snaring a customer willing to pay for sex. If she cannot earn an income as a sex worker, it is all the more imperative for her to snare a husband. She is willing to move down the class ladder to do this.

There is a double significance, too, to the idea of putting a paper lantern over the light. On a physical level, Blanche needs to soften the lamp light in the apartment so that her age is obscured. She doesn't want her emerging wrinkles to show; she wishes to look younger than she is. On a different level, putting a paper lantern over the light refers to obscuring the harsh truth about how she was making her living before she arrived in New Orleans.