Your Internet provider may give you some space to host your own website, or you can check out
thefreesite.com it has lists of sites that provide free web hosting.
As tinga81 suggested, you may have to zip or rar the file since some sites won't let you upload exe files.
Some sites have web forms that allow you to upload files, and some allow ftp or have both. If you upload a lot of files (web pages, images, etc.) ftp is the way to go. You can
download Core FTP Lite, it's free and easy to use.
If you don't know how to create a web page, most of these free sites will have some simple templates that you can use. Or if you don't know HTML code, and don't want to learn it, you can use Microsoft Word to create a web page by clicking > File > Save as web page or HTML. Or you can
download OpenOffice, it's free and very powerful.