When I upload an HTML file to my website with <a href=""> tags, the link appends the URL in the link to the end of the current URL.
For example, if my website was example.com and the index.html file was placed in example.com/test and the link was google.com then the link would go to example.com/test/google.com.
How do I make it so the link goes to google.com?
You should really learn about absolute and relative paths. What you're using is a relative path.
This is an absolute path on your server:
<img src="/images/logo.png">
This is an url with http protocol - opens Google.com
<a href="http://google.com">Google</a>
This is an url without explicit protocol, it will turn into http or https based on what your page uses:
<a href="//google.com">Google</a>
Use one of those for what you need (typically the http one).