If I decide to do something purely for pleasure, does that mean that I have clung to that pleasure?
You got it. Doing anything merely for pleasure is a trap, because like you yourself said, pleasure is the superficial appearance that quite often is a false indicator of the long-term benefits of the underlying activity.
Buddhism teaches us to not be fooled by the superficial appearances ("illusions") because they are misleading and thus conducive to suffering. To not be fooled means, to not take them at their face value. Pleasure is one such instance out of the broad class of superficial appearances that we should learn to not reify. To not reify means to not assume that the appearance is reality. In(In Buddhist context when we say "do not cling" the meaning of "to cling" there isit means "to reify", "to confuse appearance for reality", and therefore "to build a system of expectations on the illusory foundation".)
one's reasoning for becoming a monk would be for the pleasure one derives in the idea of working toward enlightenment
Yes, of course. This is an established fact in Buddhism, that the very confusion of reification is exactly what motivates us to seek Enlightenment in the first place. Reifying the imaginary Enlightenment as something awesome and cool is the useful mistake that makes the path to Enlightenment possible.
the quickest way to end both pleasure and displeasure...
...would be to stop overgeneralizing phenomena based on their identifying characteristics, to stop reifying those generalizations as something real, and to stop allowing those reifications to motivate one's daily activity.
How this can be done in the layman's world?
Getting back to the topic of not clinging to pleasure and displeasure, this means to stop confusing pleasure/displeasure on one hand with benefit or harm on the other. When you act with the long term benefit as the goal, pleasure or displeasure are not your primary concerns.