There are multiple ways to do this:

• Click on the link with the middle mouse button (if you have one)
• Press ctrl while clicking on the link
• Right click on the link, and select Open Link in New Tab.

You can click on the link or bookmark using Ctrl+click or Ctrl+Shift+click. One of them will open in the foreground in a new tab the other in the background into a new tab. Depends on your options settings.

Some items you might want to set in about:config, see Firefox configuration variables relating to clicking on a link or on a bookmark. (#newtab)
http://dmcritchie.mvps.org/firefox/keyboard.htm#newtab

You might want to try these settings in your about:config as described in the above link.

browser.search.openintab user set true

browser.tabs.loadBookmarksInBackground default false (***)

browser.tabs.loadDivertedInBackground default false

browser.tabs.loadFolderAndReplace user set false

browser.tabs.loadInBackground user set false (***)

(***) you want these two to have the same setting so opening from a link will be the same as opening from a bookmark or opening from history.

Google Search results > upper right corner gear/settings: Results Window: [x] Open search results in a new browser window.

Please mark "Solved" one answer that will best help others with a similar problem -- hope this was it.

I guess I muddied the water, because I don't recognize what you're saying as being applicable to what I want. My computer crashed a few days ago, and I downloaded Firefox. I don't know if it's the same version I had before or not. When I type in an address and press enter, that web site opens up in the furthest right tab that already has something in it. Before, a new tab would automatically open up for the new web site, so everything I opened would be visible without having to do anything. How do I make that happen?