How can you read Romeo's lines most effectively to grasp their meaning as well as their poetry?

I would suggest always reading verse (whether poetry or drama) with a dictionary nearby.  Understanding the words that one is reading is important no matter what, but it is even more critical when one reads verse because verse is a more condensed style of writing than prose.  I hesitate to say that a poet must choose his or her words with greater care than a novelist, for example, but I think it may be true because words have to pack a greater punch in verse.  There is no way to understand Romeo's language unless one understands all of his word choices. 

It is also important to read verse aloud.  Shakespeare employs meter, sound devices, and more, in order to convey tone and mood, and reading aloud helps the reader to pick up on these more readily.  Further, reading aloud causes one to slow down and spend a bit more time with the text.  This will help you to appreciate the poetry of Romeo's language as well as its meaning.