On the surface, Outlook 2010 (and other versions) seems to not have a very robust search feature. For enterprise Exchange Server 2010 using Outlook 2010, searching is easy.
If you have no sub or custom folders created under your Inbox, then default searching works well enough. Look for the Search Inbox (Ctrl + E) box. You can enter any keyword to locate emails with said keyword. But I have seen employees in companies who have created dozens and dozens of folders under their Inbox. This is done for organization purposes. I have seen some custom folders nearing or topping 100!
The advanced Outlook search feature is needed in this case, as the default Inbox search only looks within the Inbox itself, and not the sub folders. For advanced searching, try this:
Within your Outlook Home, Inbox, click the Search Inbox (Ctrl + E). Don't enter anything, just single click in it. Then open "Search Tools" near the top, and then "Advanced Find". Then in the "Look for" box, change the default selection to "Any Type of Outlook item". Enter some key words or names, and search all of your sub folders. There are a few other custom parameters to experiment with.