Well, for interpreting poems or any other piece of literature, first of all you need to understand the time. Every work is a product of its own age; if Pope would have written in Eliot's time, he would write another Four Quartets instead of The Rape of the Lock. Try to understand the socio-historical background of the work first. Analyse the contemporary, society, science and popular beliefs, economy and so on.
For example, if you are studying Wordsworth, ask yourself why that person was writing Romantic lyrics and not social commentaries like Dryden. In Dryden's time, there was no newspaper - the poets had to write pamphlets and let people know about socio-politicial scenarios. In Wordsworth's time, newspapers took over that part. Will you buy a volume of poetry about any political issue when you can know about it from newspapers? Thus, poets could, or had to, turn their focus to nature, inner selves, and mysticism.
Go through some good history of England books. There is a series by Pelican on history of England, with one volume focusing on one century. Also read European history in general. To interpret 18th century and Victorian literature properly, you need to understand the contemporary socio-economic changes before and after the Industrial Revolution.
Secondly, try to find out whether the biography of the poet can add any extra parameter to your understanding of the poem. If someone does not know that Milton was blind, he cannot interpret Samson's lament over blindness in Samson Agonistes as Milton's own lament. Similarly, if you do not know that T. S. Eliot had double hernia resulting in impotence and a failed marriage, you cannot interpret Prufrock as the daydreaming of an impotent man [Before 1970s, critics often missed the bus by interpreting The Waste Land as the epic portrait of the post War Modernist world, while it was actually autobiographical]. This approach is known as bio-historicism.
Next, try to figure out whether the words, phrasing, figures of speech, rhythmic pattern and all such ornamental things add any extra flavour to its interpretation or not. For example, if someone does not understand the English language, he can still figure out the tonal difference between Blake's "Tyger, tyger, burning bright / In the forests of the night" and Gray's "The curfew tolls the nail of parting day / The lowing herd wind slowly o'er the lea". In the first case, the trochaic tetrameter (with catalexis) clearly denotes the tone and mood of child rhymes. In the second, Grays's iambic pentameter conveys seriousness and is a perfect conveyance for an elegy beginning with a daybreak scene. This is called formalistic approach, and is especially handy to interpret metaphysical and modernist.
Many poets, especially Eliot, is often quite allusive; and if you do not understand what the allusions or references mean or symbolize, you miss the bus. It is particularly useful to have a handbook of classical (mainly Greek and Roman, sometimes Egyptian, Indian and Norse) mythologies. Edith Hamilton's Mythology and William Hansen's Handbook of Classical Mythology are undoubtedly two best books to recommend.
There are few good books available in the market to teach critical appreciation of poetry. H.L.B. Moody's Literary Appreciation: A Practical Guide is a must for every English major student. This book will show you step by step how to write critical appreciations of English poems, with pieces for practice.
Heroic, Mock-heroic, Pre-Raphaelite and Romantic poets drew heavily on figures of speech, so have some good rhetoric and prosody books. Another must-have book for graduation level students of English literature is M. H. Abram's Literary Terms.
I think these basic concepts will help you attempt your first answers and critical appreciations of English poetry. If you require to know any specific thing, write in details about that particular problem.
Statutory warning: Do not depend on popular note and guide books. They often misinterpret and mislead. Be attentive in your classes; class lectures simply have no alternative.