The problem in sonnet 18 is that everything in nature dies. The poet wants to find some great metaphor to compare his love to, but none of the traditional metaphors work. Why? Because everything in nature eventually decomposes. That's a problem because he wants some aspect of her to be immortal.
So the quick and dirty, easy way to figure out a sonnet is to separate the poem into an octave(8) and a sestet(6). Look for a "but" or a "yet" or some other turning word at the beginning of the sestet. Also look for a rhyming couplet at the end. Shakespeare sometimes messes with form, so he'll often start an apparent turn at the sestet and make his final point at the rhyming couplet. That's what he does here: first 8 lines--he'd compare her to the best of nature, but that's not good enough because nature is flawed and impermanent; at the sestet--"but thy eternal summer shall not fade..." he says that she will live forever fair (the metaphor is not entirely rejected but is being reinvented) and, finally, at the end, he says how he'll accomplish this godlike act: she'll live on in a permanent, unfading summer (her beauty will last forever) because he is writing a poem about her. And, arrogant as it sounded, in his case, it worked: his poem has long since outlived her.
All sonnets do this...the "turn" or the switch from problem or situation to answer is different for most sonnets. Petrarchan or Italian sonnets usually "turn" after the first eight lines. Sonnet 43 "How do I love thee" by Elizabeth Barrett Browning is one exception since her Italian sonnet begins to "turn" after the first line.
English sonnets--either Shakespearian or Spenserian (Edmund Spenser) turn after the first 12 lines.
I like to call the "turn" the BIG BUT. The turn is usually begun with some transitional word or conjunction like yet, but, so, etc.
So, read your sonnet a min imum of 3 times. First for the content--get the gist of the poem. Second, for the problem and the solution (the turn is in there somewhere...look for the big but) Third for the rhythm and sheer beauty of the language. The more you read those 14 well-constructed lines, the better you'll understand them and the more you will learn to love poetry.
You are correct. Sonnets are structured so that the first part presents a problem or asks a question, and the second part provides an answer or solution. In Sonnet 18, the problem presented is that summer is not a sufficient way to describe the beauty of the woman Shakespeare is talking about. He is trying to find a way to describe her beauty, but in the first 8 lines he lists off all the reasons why comparing her to a summer day doesn't work. She is more beautiful, more fair, etc. In the last 6 lines, Shakespeare offers the solution that her beauty will be praised for eternity within the poem he has written.