Considering the title, the poem might be about art; it may be about one specific type of art.

The poem is arranged into six stanzas of three lines each, while the last stanza is made of four lines. So in the poem we can identify five tercets and one quatrain.
The sentence “The art of losing isn’t hard to master” is repeated in stanzas 1, 2, 4 and 6.
The word “disaster” is repeated in stanzas 1, 3, 5 and 6.

The rhyme scheme is ABA, and ABAA in the last stanza, whose first line is more an example of consonance than rhyme (gesture vs faster/vaster/disaster), but it more or less reproduces the same sound as in the previous “A” lines.

The speaker address a ‘you’ that losing things and people is part of life; we become masters at ‘the art of losing’ and learn that life tends to go on as before, although any loss may initially be experienced as disaster.
The speaker is talking about how easy it is to lose things and loved ones, due to distraction, loss of memory, lack of time, exile, the end of love, or death.

The methafor of "losing" as an "art" runs through the poem suggesting that losing things is not so important, but losing people and significative conditions, such as living in a certain place or house, is much more serious, and we need to learn the "art" of survival after a loss.

The register is fairly informal, as shown by contracted forms (“isn’t”, “wasn’t”) and the direct address to the listener/reader through imperative and the pronoun “you”. There are some common words such as “places”, “names”, “houses”, and most of the vocabulary belongs to everyday language.
Common situations like losing a watch or keys, or wasting time, are easy to imagine. It is more difficult to visualize losing cities, rivers and people.

The poem itself can be read as a metaphor: “One art” may suggest that the art of losing and the art of writing poems are one and same. We refine our ability to lose things, making it an “art”.

In the poem there are two assonances:

• I. 1: “The art of losing isn’t hard to master”;
• I. 8: “places, and names, and where it was you meant/”

In line 2 and 3 there is an alliteration: “so many things seem filled with the intent /to be lost that their loss is no disaster.”

There are five enjambment in lines 2-3; 4-5; 8-9; 11-12; 16-17.

Considering the verbal forms, the present is the most prevailing tense.
There is just one passive form in its full form: “to be lost”; a few implicit forms: “lost door keys”, “an hour badly spent”.
The imperative forms are: “Lose something”; “accept the fluster”; “practice losing”; “look!”; “Write it!”.
Finally, affirmative is the main sentence type.