You can only delete your own posts, and only if it is the last post in a thread.
If both of those conditions are met, there will be a button with an X somewhere on your post (different places depending on the theme you choose in your profile in your user control panel
). In the subsilver-type theme, it's in the lower right corner of that post.
If anyone has posted a reply after you post in a thread, you can't delete your post anymore.
You can still edit it.
BTW, since your question has nothign to do with search problems, fixes, or suggestions (about searching), I'd like to move it to its' own thread in the Forum Rules and Features section.