I would recommend 'Understanding Poetry' by Robert Penn Warren and Cleanth Brooks, as a good introduction, it also includes a reasonable collection of poems from various poets to appreciate.
I would also suggest getting an anthology like 'The Golden Treasury' or Anthony Quiller-Couch or Robert Penn Warren (Six Centuries of British Poetry) or G B Harrison. They are available often in small pocket editions, which one can carry around with one.
I've been reading "Sleeping on the Wing" on and off recently -- I think it's meant more as an intro for older school kids but I've never read poetry outside of school and it's been an interesting overview of different poets and styles.
I would also suggest getting an anthology like 'The Golden Treasury' or Anthony Quiller-Couch or Robert Penn Warren (Six Centuries of British Poetry) or G B Harrison. They are available often in small pocket editions, which one can carry around with one.