What does (in firefox) File->Print Preview display? Does it look right?
Select (in firefox) File->Page Setup. Does what's displayed look right?
Select (in firefox) File->Print and look through all of the tabs to see if anything looks wrong. Is your printer the one selected under the General tab?
If you run
lpstat (from a console) immediately after printing something to your printer, what does it say?
What happens if you select "Print To File"? Do you get a file saved?
If you do, what happens if you send that file directly to your printer with
lp filename or
If you use CUPS (most systems do), what do you see for the printer information?
localhost:631/printers in your browser address bar and select the entry for your printer. See if everything there looks OK.
Does it show your current/recent print jobs in the print queue near the bottom of the page? You can post the output here if you're not sure.
If you have or can borrow another printer, does Firefox print to that?
I've had printing do nothing for certain postscript files (from printing to postscript file from inside acroread). It also happens if your printer is "dumb" and requires a firmware download before printing. This is the case for HP1006C and HP1020 Laserjets, but I don't think inkjet printers have that "feature".
Since it's Firefox, try entering
about:config in your address bar. That will take you to the Advanced Configuration screen.
Put "print" in the search bar and scroll down through the (many) entries that are still displayed. Look for entries that contain the name of your printer. (Once you see the actual name that is used for your printer, you can just search for that the next time you need to venture here.)
Are there any entries for your printer at all? If not, then that's a big problem that I don't know how to deal with, but it's a good place to start asking a more precise question.
There should be two types of entries. One type is about defining the printer and will start with printer_yourprintername. ...
The other type is about how some of the options are set right now and will start with print_tmp_printfeatures_yourprintername. (For now, ignore these.)
If they are there, are the entries right? This is pretty much a rhetorical question because there are a ton of them and it can be really hard to figure out what a lot of them mean at all before you even get to whether they're right or not. Look for things like whether it thinks it needs to download firmware, whether it has a definition for the size of paper you use, and whether it says anything about using a paper source (tray) that you don't have.
The whole about:config screen is not selectable or printable :( , so if anything looks funny or you just can't figure it out at all (It took me several years of flailing to understand what just a few of the settings do), you may want to copy the whole thing up to the web where we can see it. It should (usually) be found in
$HOME/.mozilla/firefox/(some_random_string).default/prefs.js which is a plain text file.
For now, don't open it with an editor. It has a few very long lines and gets overwritten every time Firefox closes.