In the poem, the speaker lists a range of things we lose, from very trivial instances to very significant losses. Everyone loses things and in this way everyone has practice at this skill. With any art or any skill, the idea is that the more you practice that art, the better you will become. In the second stanza, the speaker instructs the reader, herself, or some other person to practice losing:
Lose something every day. Accept the fluster
of lost door keys, the hour badly spent.
The art of losing isn't hard to master.
The speaker continues to encourage the practice of losing because in the end, losing things is inevitable: "so many things seem filled with the intent / to be lost that their loss is no disaster."
One interpretation of the poem is that the speaker suggests (and/or is trying to convince herself) that with enough practice at this skill of losing, one will be better able to handle the significant losses in life. However, in the last stanza we see her reluctance to even write that losing her lover looks like "disaster." From this reluctance, the suggestion is that losing trivial things is easy to master, but the practice of losing those things can not really prepare you for the loss of more meaningful things and people. Thus, the art of losing a loved one is easy to do (because it is usually beyond our control), but dealing with that loss is not easy to master. It is therefore, an art. Fittingly, writing poetry is a way of dealing with loss: the command "Write it!" is the illustration of the poet using art (writing) to deal with a loss.