Hi,
I've a file which I'll download from my client's site and save it on my hard
disk, and import it to the same database table every friday.
I want to make this process automatic. So, I went online and searched on
this issue.
And I'm pretty much convinced that DTS could do this. I went and read some
tutorial in sqlis on how to create a package (I'm using sql 2005).
I created a package which will import the data in the file to the specified
database when I execute the package. But how to make it automatically run
when ever a new file is added to the 'file folder' which will over write the
old file in the database and sends me an email saying that the new file is
being imported?

You could use Alan Mitchell's custom File Watcher task
(http://www.sqlis.com/23.aspx) or have a .NET file watcher in code.
Alternativley you could just run the package regularly (schedule as a job) to
poll the directory.
There is an email task and you can use a precedence constraint to ensure the
email is sent on successful copletion.
HTH,