Hi Davy and welcome to the forum.
If you have already downloaded some Music Finder Database files from the internet to your PC, then the easiest way to transfer these to to your T4 is via a USB memory stick. You start by simply copying the files to the USB using Windows Explorer or whatever you use.
Then plug the USB stick into either of the two USB 'to device' sockets on the T4, the front one is obviously the easiest to get at. If the T4 is already switched on, you should see a message on the screen saying 'Device is connected'.
Now open the Music Finder by pressing it's button. You will see some icons at the bottom of the screen above the pairs of buttons that are associated with them. Above the number 7 buttons is 'FILES'. This is the key to either loading a file into the MusicFinder, or generally managing MFD files, including copying them from the USB to the T4's internal Hard Disk for example. When you are in the selection displays, all folders will be listed followed by any MFD files. Files of other types will not be listed.
If you want to load one of the files into the Music Finder, press FILES and use the two 'TAB' buttons at the top right of the display to move to 'USB1'.
Find the file that you want to use on the USB, select it by pressing the relevant A to J button. A message will appear asking if you want to 'REPLACE', APPEND' or 'CANCEL'
REPLACE will replace the existing records in the MF with those in the new file.
APPEND will add the records in the new file to the existing ones in the MF (as long as there is enough space - maximum number of records is 2500).
Just press the relevant button and after confirming what you want to do, the new file should be loaded.
If you want to make a copy of the records that are currently in the MF before you change the file, press FILES, tab to USER, HD1 or USB1, select a folder if required, and press 'SAVE'. You will get the opportunity to name the file and when you have done so, press 'OK' and the file will be saved.
If you want to just copy some MFD files from the USB to the T4 HD, press 'FILES', tab to 'USB1', press 'COPY' (Lower 3 button), then select the file or files and press 'OK'. If you have several files in the same folder, you can select all of them by pressing 'ALL'
Now tab to the new location, e.g. 'HD1', select a folder if you have made one, and press 'PASTE' (Lower 4 button). The files should be pasted into the new location and can be selected from there when you want to load them into the MF.
You can find MFD files on the internet at various forums, or you can get them from Yamaha by connecting your T4 to the internet using 'Internet Direct Connection'. If you already have a broadband internet connection in your home, then you will have a router, either wired or wireless. If the keyboard is close enough to the router, you can simply connect the two by cable from the network socket on the back of the T4. If this is not practicable, then you can buy a wireless LAN adapter to plug into the T4.
Note that however you connect, you will only be able to access one single website.
Although there are additional MFD files available from the site, I personally don't think that it is particularly useful for anything else. You might like to try it first using a simple cable connection (temporarily moving the keyboard if necessary) to see if it is worth while setting up a wireless connection.
Finally, you don't need any expansion memory to use new MFD files, or for tha matter external Styles, Registrations, Multipads, Audio (MP3 or WAV) or MIDI songs.
You only need it if you want to add new Voices that contain wave samples that are not already in the instrument. These include Yamaha Premium Voice Packs as well as 'UVN' voices from third party sources, either free or purchased.
I can't see what harm it will do to register your T4, and if you ever do decide to fit the expansion memory and buy Premium Packs from the Yamaha MusicSoft site, you will have to register it there anyway.
Finally there is a lot of references in the Owner's Manual saying 'For more information, refer to the Reference Manual on the website'.
It is well worth downloading a copy of this which is available, along with other files such as USB/MIDI drivers if you need one, from the page in the following link...
Tyros4 - Yamaha Downloads UK and Ireland