Activity, Sequence, and State Diagrams are all correct ways of showing thread behavior.
1st: (To vs's comments) There are two sets of diagrams or modeling elements in UML, static structure, as you put it, and behavioral. Any book will help you understand the split, typically in the contents/TOC, additionally it can be seen on page 11 of Martin Fowler's UML Distilled a near defacto standard for beginning UML in my opinion.
2nd: (To sipwiz's question and comment) Activity diagrams are not commonly understood to model business process, they can be used for that however, and most examples or simple tutorial would approach it from a business standpoint.
Discussion on your options to model threads:
Activity diagrams - Allows for forking and specifying concurrency by using a BAR and usage lines. Note the example at the bottom is no a business process, example. Most people can read these, business, management, and developers, though sometimes they can lack detail or get messy.
Sequence Interaction diagrams - In the same post, example, you will see sequence diagrams allow you to specify parallel behavior within a sequence by boxing parallelizable behavior with a label "par", this is useful to show the reader what methods can or should be called in parallel, ie, by different threads. This is the method I would use for detailed developer like discussions around building an object.
State diagram - The state chart just like the activity allows for concurrency by using a BAR and usage lines.
NOTE: These will not model a specific thread and it's exact lift cycle, as that is part of the instance/run-time level of modeling, if this what you want clarify your question and I will respond. I would just model it using one of the above as no one other than a MDA/UML expert will call you out, and you are not generating a running system.
Also: Please note that further details can be found in most UML books.
Also leveraged: http://www.jguru.com/faq/view.jsp?EID=56322