Microsoft Word (which actually comes as part of the Microsoft Office 365 package) is only free to students who purchase the software through their school.
If you think you think you might be eligible for a free version, then check out this page: https://products.office.com/en-us/student/office-in-education
Alternatively, I would recommend using Word Online: https://office.live.com/start/Word.aspx
It's not as powerful as the full MS Word suite, but it's almost identical!
I can also recommend Google Docs.
I actually use Google Docs all the time, it's very convenient if you often need to share documents with others and co-edit.
You can learn more here:
http://www.google.com/docs/about/
What I would
not recommend is downloading free versions of MS Word from websites that aren't affiliated with Microsoft.
A quick Google search shows that there are a bunch of other websites that claim to offer free downloads of Microsoft Word, and other Microsoft programs. Personally, I wouldn't trust them and don't recommend downloading anything software from them, as they could contain malware.
Play it safe, and use the options above instead.
Happy word processing!