I agree with Amit regarding the use of rel="nofollow" to disavow potentially poor quality links from your website, protecting its reputation, however I don't think this is all you need to accomplish what you were asking.
Regarding 'nofollow', it causes Google to drop the target links from their graph (or view of the web) however, they may still appear in Google's search results if other sites link to those pages which you will have less control over. Also, other search engines may handle nofollow differently so it is not a catchall solution.
To prevent all "robots" from indexing a page on your site, therefore allowing your other pages to take a higher status place the following meta tag into the section of your page:
<meta name="robots" content="noindex">
OR to apply the 'nofollow' directive to all links on that page use the following;
<meta name="robots" content="noindex, nofollow">
When search engines see the noindex meta tag on a page, they will (in most cases) completely ignore the page and drop it from their search results (at least Google and most major ones do), even if other pages link to it. Once again, other search engines may interpret this directive differently but most wil indeed ignore the page.