How to refill an Epson printer Cartridge T0881 Black ink, have the set although instruction do not include this model.

Did you refill the cartridge? If so, then you will need to reset a chip on the cartridge somehow. Usually epson doesn't sell "refill" ink unless it is an EcoTank series printer.

Yes
http://www.epson.com.au/products/multifunctional/stylusnx125_specs.asp
but you can buy one yourself for less than $5.

Follow these steps:
1.
Buy an Epson ink refill kit. A refill kit gives you all the tools you need to refill Epson ink cartridges. Kits typically include a syringe, rivets, ink, and instructions on how to refill the cartridge. You can find Epson ink refill kits on the Printer Filling Station along with instructions for each specific model (see Resources).
2.
Cover your workspace with a paper towel and fill up the syringe with the ink color you need. Epson refill kits will either include black ink or the color combination cyan, yellow and magenta. On average, you'll need 10 ml of black ink or 5 ml of color ink for Epson ink cartridges.
3.
Find the rubber seals on the back of the Epson ink cartridge. Insert the rivets into each seal.
4.
Empty the contents of the syringe into the Epson ink cartridge. You'll want to perform this action slowly in order to avoid spilling or overfilling the cartridge.
5.
Remove the rivets. Use tape to cover the holes you made in the ink cartridge. Return the ink cartridge to the printer. Allow the printer to go through several print cycles in order to ensure that the Epson printer operates properly.

In case of any additional help please revert back

You should be able to refill the cartridges with no problem I do it all the time on a variety of different printers, I'm not familiar with that particular model, I am guessing that you are in Australia, here is a quote from their page for your printer:
"This printer is designed to be used only with Genuine Epson Intellidge™ ink cartridges
Intellidge™ Ink cartridges are not designed for refill."

So I am really not sure hope that has been some help.

If this helps, with the Epson C40 Stylus here in Canada there is only two cartridges black and one for the the colors if you rub your over the sticker if there is one towards the back of the cartridge it should show an indentation this is on the C40 cartridges, this is where you fill the cartridge, same on the black I believe, that or may not work for you.

Don't let your ink levels drop below 25% before refilling and resetting your cartridges. There is an inner and an outer chip on these cartridges. The inner chip disables the outer chip when it's contacts are no longer bathed in ink. So, it doesn't matter if you "reset" the outer chip after refilling your empty cartridge because the chip was disabled. I'm really curious how you refilled these cartridges yourself without souring yourself on refilling from the experience. I own a Cartridge World ink refilling store and I refilled a set of these cartridges when we had replacement chips available (we don't now because our chip distributor was violating Epson patents) and it was an absolute mess, took forever, and the cartridges still didn't work in our test printer.

You can do a search on Google using "Epson C84 Refill Instructions" which will produce plenty of hits. However, this one gives very clear instructions:

http://www.refillinkcartridges.co.uk/news/2008/10/16/epson-c84-ink-cartridge-refill-instructions/

If you only bought refill ink rather than a refill kit, and don't have rubber plugs, you can successfuly re-seal the filling hole using a small amount of epoxy resin e.g. araldite. This is easy to remove with a sharp knife the next time you want to fill it. Note the need for a cartridge re-setting tool - these can be purchased very cheaply on E-Bay.

EPSON Support page for your printer including manual:

http://www.epson.com/cgi-bin/Store/support/supDetail.jsp?BV_UseBVCookie=yes&oid=41661&infoType=Overview

the ink cartridges for an epson stylus dx4400 are unrefillable,you have to use genuine epson ink with this printer.i have the same printer.you can buy a single black epson cartridge from asda,comet,tesco and other big well known stores.do not use other,cheaper copy cat ink cartridges as it really does ruin your printer.

The printer will never do that, once the cartridge is spent a little divine device inside tells the printer it's been used and spent. You can still print to from the cartridge but it wont warn you when your low on ink, price you pay for not buying a new cartridge.

By using Colorbyte's Imageprint software and their 'Phatte Black' cartridge.... 
www.colorbyte.com
I have not purchased it myself quite yet but im good friends with an Epson R&D guy who tested their system and highly recommends it.