You're done with the title and abstract screen and you're faced with a list of dozens or even hundreds of articles you have to retrieve. What to do? It's a time consuming process, no matter what (hey, you said you wanted to do a systematic review, right?). If you're using Covidence, you can export the selected records into EndNote or Zotero, as this will make the process easier. When you've got them all you can upload the pdf files back into Covidence in bulk. The following steps will make the process of collecting the pdfs more efficient and thorough.
You'll still be left with a lot of pdfs to get, and you'll have to work one reference at a time. To make this efficient, you should make use of Harvard Library tools that either take you to the pdf or automatically give you the option to request a copy through the library's Interlibrary Loan service. You can use either Harvard Library's HOLLIS catalog or PubMed (Make sure you start at the Countway's Web page). HOLLIS may be the better choice as it contains material that is not included in PubMed.
The above steps will get you most of the articles. If your ILL request comes back or finds nothing, check the citation. You'd be surprised how many are incorrect. Even a mistake in the issue or volume may result in you not getting the article. If you need help at this point, it's best checking in with a librarian.