Searching on the "open web" in this context simply refers to searching outside the curated experience you might find within a library's holdings, stepping out beyond paywalls and subscription fees that academic libraries maintain to provide trustworthy, credible resources. There are certainly trustworthy sources outside Salmon Library, you'll just need to really leverage those information literacy skills to find the "good stuff", but you need to be doing so at all times anyway! Always be evaluating what you find online (remember the rhetorical triangle evaluation cycle), and pay special heed to the Domains of the websites you encounter. While exploring multiple viewpoints is critical to achieving a more comprehensive understanding of an issue, try and shy away from your .com websites when possible. Try and explore sites ending in .edu for educational institutions, or perhaps .gov for federal and state level publications, or even .org for potential non-profit organizations or research institutes.
There are also a handful of open access databases and information repositories that we can recommend, depending on your topic. The below are two very credible, trustworthy initiatives in open access scientific literature. The journals indexed in each of these are peer-reviewed but also freely available to the public. Such initiatives with true credibility are fairly rare, so take care and ask a librarian if you are ever unsure!
The following are examples of open access platforms hosting only pre-print articles, so not peer-reviewed as of yet:
The following are open access platforms for publishing articles and data, a blend of pre-print and "published" information: