On the top right corner of any ListView page is a search  box. That box
is scoped to searching the list that you are on. So, you should be able
to enter the document  name there and get back the results that you are
looking for.

Note, the list search is subsequent to the ListView that you are
searching against. So, the columns that will be returned, their initial
sort order, and the filter that is defined in the view will be used in
conjunction with your search.

I have tried your suggestion and it works fine
but before sometime, a guy told me something about 'crawling' and
'keywords'. What can we achieve using these?

Those are SPS Search terms and only available from a SharePoint portal
(or its API).

I also believe that the trick that Todd suggested works on the current view of the document  library (i.e. the list). It would not search  in the folder and subfolders... just the current view.

When I an trying to search  a file using the search textbox, it shows
document(s) by that name but also shows other lists, etc. How can I
restrict my search results so that it gives me only documents?

If you are getting both listitems and documents, you must be using the
Web search  on the default.aspx page rather than the search box on the
ListView page (like AllItems.aspx).