You need to be able to make a bootable disk (either a floppy or a bootable optical disk) that you can boot from into some version of DOS. Then they want you to put onto that bootable disk the software contained in the .zip file you download from Samsung.
Now, on a floppy disk (if you have such disks and a drive on the machine, even temporarily) it's not hard to make it a bootable DOS floppy with some empty Free Space left. Then you can un-ZIP the downloaded file and have the resulting files placed on that floppy. You're ready.
BUT for many people now who don't have any floppy drive, the solution is to make a bootable optical disk that must have ALL the requisite files on it. This means you must be working from a machine that CAN boot from an optical disk - most today can do that. You ALSO need some optical disk burning software package that can burn a bootable CD with the correct DOS files in the correct locations. The trick, though, is that it can be very hard to add files to an existing optical disk, depending on how you burn it. The easier procedure might be to un-zip the downloaded file into a temporary subdirectory and gather there all the files you might need on this CD. Then burn ALL of those files to the CD in one operation so you don't have to add to it later.
Now, you boot your machine from this disk (floppy, or optical) and it will load DOS into RAM and be ready to run commands. Then the instructions are to execute the program called "Patch" that is on that same disk. DO NOT TURN OFF during this operation - wait until it completes and returns to the DOS prompt. Then simply shut down the machine, remove the bootable disk you made, wait at least 10 seconds, and power up again. This sequence will write the updated firmware to the F3 hard drive.
I note it specifies that the drive you are updating must be connected as the Master device on the Primary IDE port - apparently that's how the updating software was written. I presume - I did not check - that your HDD is an IDE device. In fact, I would be very tempted when you do this to DISconnect any and all other hard drives in your machine just to be absolutely sure the routine cannot write to the wrong HDD unit. After the update, reconnect all drives as they used to be before powering up.