It is true that you must relinquish all attachment. This cultivation is part of The Way (to enlightenment) and you should keep in mind that the body is an attachment only released at natural death.
Nonetheless, you must relinquish not only "attachment" but also attachment to the act of relinquishing attachment. How? The understanding comes from insight and wisdom, which harmoniously develop together as you read, contemplate, and meditate the teachings and your own situation.
Really, the idea of "attachment" is at its very base concern for self. As you live more selflessly, and thrive in the happiness of other sentient beings, it will be easier to detach, as you will increase awareness and mindfulness.
There are the precepts, which hold you from wordly and gripping attachments. By holding the precepts you are slowly released from karmatic bonds that would otherwise prevent you from even being able to understand and look for meaning in the Dharma. Naturally, you are experiencing a clarity of mind that is well-afforded by virtue and merit, and you should continue to cultivate.
What does it mean to cultivate?
In order to relinquish all attachment, one strives with vigilance to see all marks as no marks. One also strives to relinquish all attachment that is visible from the 'ego' or 'self'.
The Buddha taught Dharma because although one is capable of relinquishing attachment to what one directly "observes," one is incapable of relinquishing that which one does not know she/he is clutching. Your fist is clenched very tightly and you are holding something. Oh, what a grip! It is impossible to let go.
Imagine your surprise when your fist unclenches and there is nothing there. In a similar way, one clings to perception. The "information" from your eyes, nose, tongue, ears, body, and thoughts (as well as emotions) is ephemeral (temporary). It all passes because it all changes. Everything changes and nothing is permanent. To contemplate these thoughts is to contemplate Dharma.
How does one let go of "attachment" ? How do you let go of "letting go" ?
"Letting go" is just a concept. Really, there is nothing to let go of because you are not holding on to anything. The Buddha taught that our clinging is a consequence of Doubt, which arises from causes and conditions. Doubt is not real, and in trying to avoid doubt (rather than investigate it and understand that it is empty) sentient beings cling to that which feels good and comfortable, and avoid that which is "bad" or feels uncomfortable. Truly, the more comfortable you get at understanding that nothing is comfortable or uncomfortable, the more you will see.
Really, the attachment to physical objects is coarse. It is several steps removed from the very basis of attachment, yet they are the same entity. It is all one entity and it is all no entity, because there is no entity. Words do not suffice to explain concepts which are only truly received and understood at levels "between frames of time" -- as it is necessary for you to observe this "in motion" in order to understand what it "means," but the understanding and wisdom that liberates comes from within.
True attachment is not only the physical world -- it is the conceptual world, the emotional world, the perceptual world. Consider that you are sitting at a "desk" -- really it is no desk at all, it is just materials aligned in a configuration -- but again there is no material, it has no inherent existence of its own. It is constantly in flux and always changing, and your attachment to the label of "desk" is merely an attachment. Naturally, we cannot deny the reality around us, but we can strive toward understanding that it is all one fluid. Then, pondering that there is no fluid, that we are the fluid. Understand that there is no separation between "self" and "other" because we are all one fluid.
With the motivation to be happy and free of attachment, to be free of suffering, it will become more and more effortless to see, feel, understand, and speak true Dharma. Patience in the ways of suffering is of measureless virtue and merit. Your mind is brilliant -- like "a blue sky filled with white light" -- but it cannot answer a half-baked question. No matter how correct, if you don't know what you are asking then no answer will be of use to you. Thus, I recommend working with what you are trying to wrap your head around at the moment, and letting the true question form over time. In my case, I have found it helpful to ponder and meditate on such things as "What is attachment?" -- work with your mind to perceive and exist in the current singular moment. There is present, past, and future, as is taught in Buddhism, but really you cannot ever truly dwell in the "past" or catch up to the "future" because all concepts are attachments.
When leaving the world of concepts, recall your ambition to feel happy and to "embrace" liberation. We are all one intellect, striving to unify. May we all, in the last words of the Buddha (really the physical body is just a form, and death is a transformation), strive with vigilance.
love and wisdom, my friend and eternal brother.