To search for files in File Explorer, open File Explorer and use the search box in the upper right. (Note that My Computer was renamed to This PC in Windows 8.1 and Windows RT 8.1.)
Open This PC by swiping in from the right edge of the screen, tapping Search (or if you're using a mouse, pointing to the upper-right corner of the screen, moving the mouse pointer down, and then clicking Search), entering This PC in the search box, and then tapping or clicking This PC.
Search looks in all folders and subfolders within the location you're viewing.
When you tap or click inside the search box, the Search Tools tab appears. As you enter your search terms, your results will start to appear with your search terms highlighted.
Here are some other things you can do with the search box and the Search Tools tab:
To search for all files with a particular file extension, such as .txt, you can enter your search term like this: *.txt.
You can search for a file based on properties such as the date it was last modified or what kind of file it is (such as "Picture"). After you enter your search term, tap or click the Search Tools tab and use the options in the Refine group, and then enter your search terms in the search box. For example, if you want to search only file names and not file contents, tap or click Other properties, choose Name, and then enter your search term.
If you can't find what you're looking for in a specific library or folder, you can expand the search to include different locations. When the search results appear, tap or click the Search Tools tab, and then choose an option under Search again in. (Some options might not be available in Windows RT.)
If search results don't contain matches from file contents, the location you're searching isn't in the search index. To include file contents for a single search, tap or click the Search Tools tab, tap or click Advanced options, and then choose File contents. To add the location to the index so that file contents are always included in searches, tap or click the Search Tools tab, tap or click Advanced options, and then choose Change indexed locations.
For info about using the Search charm, see How to search.