If you have the default PostScript font files around you are in luck. But most users don't and they need some replacements. The replacements could be very compatible, but mostly the printed result looks a little bit different than with the original fonts. And it depends how close a "little bit different" is compared with the original font.

With the help of fontconfig you can define a mapping from the original PostScript font to its replacement on your system.

A few examples:

A font close to the default Helvetica is Nimbus Sans L. To force this font to be used if the documents calls for Helvetica, add the following rule to the fontconfig configuration directory:

 <alias binding="same">
   <family>Helvetica</family>
   <accept>
      <family>Nimbus Sans L</family>
   </accept>
 </alias>

A font close to Times New Roman is Nimbus Roman No9 L. The following rule forces it:

 <alias binding="same">
   <family>Times</family>
   <accept>
      <family>Nimbus Roman No9 L</family>
   </accept>
 </alias>

And for Courier New a close replacement is Nimbus Mono:

 <alias binding="same">
    <family>Courier New</family>
    <accept>
       <family>Nimbus Mono</family>
    </accept>
 </alias>

After having these rules in place (usually in /etc/fonts/conf.d), running the following commands show if they work as expected:

 $ fc-match Helvetica
 NimbusSanL-Reg.otf: "Nimbus Sans L" "Regular"
 $ fc-match Times
 NimbusRomNo9L-Reg.otf: "Nimbus Roman No9 L" "Regular"
 $ fc-match "Courier New"
 NimbusMono-Regular.otf: "Nimbus Mono" "Regular"

If the rasterizer queries for the original PostScript fonts, it will use your defined replacements instead.