In EBSCO, look for a link on the right side of the screen that says, "Permalink".
Here's a screen shot of the EBSCO link provider:
Note that EBSCO doesn't always provide the full text, and the permalink can only link to what's available.
In this case, the address in the browser works. This is the easiest to grab, and if you're off-campus, the proxy is included.
The DOI also works, if you right-click and copy the link; you'll need to add the proxy prefix.
ProQuest doesn't always provide the full-text of articles. To link directly to full text, go to the site that provides it and find a link there. If you link to the index record for the article, it will find the ProQuest database, where you can use Get It! Trent to link to the article, but that's adding extra steps.
If the full text is within ProQuest, go to the bottom of the record to find the "Document URL". Copy the link provided.
Here's a screen capture:
Look for the link to the "Full Text (PDF)" and copy it by right-clicking on it. Choose "copy the link" (or whatever wording your browser uses). This is the link you'll use. If you're off-campus when you connect, the proxy is included.
The bottom of each record includes a box labelled "Permalink". This is the easiest one to grab - just copy it! And if you connected from off-campus, the proxy is already included.
The DOI may also work, but it probably links to a different site; be sure to right-click and copy the complete link - it's longer than what's displayed on the page. The proxy should be included if you connected from off-campus.
In this case, the address in the browser is a durable URL. It's easy to grab and it includes the proxy if you connected from off-campus.