Let's make things simple:
1. Make sure you do not have any HP Printer related driver/software installed on your computer.
2. Click here
to download the necessary software and drivers for the HP F4180.
3. On the HP download page you now see, you only need to consider categories 2 & 5, one for the drivers/software and the other to diagnose problems, if any.
So essentially you need to download this
4. Once the download is complete, be sure to install the software and drivers as per the instructions provided.
5. Connect the F4180 to your computer and wait for it to detect the same.
6. If you are still having trouble, do consider the diagnostic software from category 5.
By the end of this, you should be printing away!
Let us know if you have any questions.