How to let go of attachment

Why do you want to get rid of attachment? 

It is because it gives you pain. If it did not bring you pain, you would never think of getting rid of attachment. Attachment gives pain because of ignorance.
Do not try to get out of attachment. Instead, I would say, learn to be centered. Expand your understanding of life and of this creation. Then you will see that you do not need to make an effort to get rid of attachment. It will automatically go away.
Young children are so attached to cotton candy. If you keep a sweet before them, they just want to grab and eat it. But when they grow older, the craving for sweets and toys drop off by itself. They did not have to make an effort to get detached from that. 

Detachment is a very natural happening.

When maturity blossoms in you, an expansion begins to dawn within you; that is when you stop getting stuck and entangled in small petty things in life.
Otherwise, earlier if someone ill-treated or insulted you, you would get so hurt and keep a grudge in your heart for a long time, sometimes even for months at a time. You would tell yourself, ‘I am never going to forget how that person treated me’. Why do you want to harm yourself with such thoughts? We do this so often, and many time, we feel proud about keeping a grudge in our mind. This is foolishness.
You should observe and accept that different people have different ways of talking, different behaviors, and different approaches to doing things and expressing themselves. Do not think that because of this they do not have any love in their heart. It is not so at all. It is just that you may not be able to see it, or that they may not be able to express it in a proper way.
Just look at things from the other’s perspective.