Robert: 587 starts in the vineyards just outside of Corniglia, but mostly it's forest and simply a way trail up the mountain, so it's quite steep in parts. Once you get on 586 and start contouring the mountain, it's all easy. You get great views back to Corniglia looking over Vineyards (my favorite views of Corniglia were from this hike). Shortly thereafter, you come out of the woods and start walking on trails that cut right through some vineyards with grand, unobstructed views of the Ligurian sea. Later in the hike--maybe around Volastra--there are some olive tree groves, which are great to walk underneath. Of course, once you get in to Manarola you should definitely hike the short vineyard trail there (you can find this in the RS guide), which will take you around to the cemetery. For my money, the best view in the whole CT is from this cemetery ... https://www.flickr.com/photos/jpkand/14839148119/
ps- If you're looking for a restaurant when you get there I'd recommend Aristide... eat upstairs if it's open and enjoy the best panna cotta you might ever have
edit: I should mention that when we were there last year they said they were in the process of switching the trail numbers to those that we've been using in this thread. However, all the signage we saw on the hikes corresponded to the old numbers, so just in case you might want to have those in mind as well. Something like this, so we've been talking about trails 7a and 6d: http://cameronpiper.com/wp-content/uploads/2013/04/CinqueTerreMap.jpg