The following is an excellent guide to understanding Ukkonen's linear-time suffix tree construction algorithm.
1. Read my blog post on why suffix trees are useful here.
2. Read my blog post on the basic definition of a suffix tree here.
3. Watch a video on Ukkonen's algorithm here.
4. Read this post on StackOverflow, which is in layman's language.
5. Read Chapter 6 of Gusfield's book, which is in technical language.
By the end, there is no doubt you will fully understand the suffix tree + Ukkonen's clever construction algorithm!