A user-friendly tool for creating saved copies of web or social media material that can be stored on your own computer is ArchiveWeb.Page. Unlike working with the Wayback Machine, this tool creates copies that you have control over, can choose to share with others or not, and can delete when you're finished.
ArchiveWeb.Page requires you to spend more time running the software, but gives you more control, and works better with dynamic web content and social media.
It is available as a Chrome browser plugin, or as a standalone app.
First, navigate to the page you want to capture in Chrome (with the plugin installed) and press "start," or press the blue "start recording" button in the app and past in the URL.
When you start recording, the page will reload. ArchiveWeb.page is now saving all this newly loaded content to your local computer. You can access progress information in the top right corner.
Once the page loads fully, you can engage with interactive elements, or navigate through the website, keeping an eye on the progress box, and monitoring the size of data stored. Once you've viewed everything that's important to your collection, press "stop."
If you are using the browser extension, you can press the "home" button to bring up a screen with access to all your recorded websites. Or, you can navigate the list in the app. You can replay any of those recorded sites by clicking on the blue link.
Browse through your captured pages. They should display and function the same as the original site. If not, you might want to try the capture again, clicking on links and making sure that all media loads.
These are saved on the hard drive of the computer that you're using, so if you're using a shared computer or want to store the files somewhere else, you can download an entire site (or set of sites) as a .WARC file.
Downloading as WARC 1.1 will work for most practices. That will create a special type of zip file that you can then share with others or upload to other storage.
You can delete locally saved web information from within the app/browser extension.