Disclaimer: This is MY way of doing things and works FOR ME, others may do things differently. There is not "one true way", so find what works for you.
There are commercial nib cleaning solutions available for purchase, however I've never used one as I don't really see the point. I consider my nibs disposable items and I fully expect them to deteriorate over time, needing to be replaced. That's not to say that I don't try to keep them in good condition, so here are my tips for cleaning metal nibs.
After use I either swish my nib in the rinse-water jar I've been using or use a pipette to squirt water over the nib, but I'm not overly concerned with getting all the ink off the nib. Afterwards I take the nib out of the pen holder so that it can be fully cleaned and dried. My next step is to take a Q-tip and dip one of the ends into rubbing alcohol (both can be purchased in any pharmacy or supermarket), then I use that wet end to thoroughly clean the nib surface. Using a Q-tip allows you to get into all the nooks and crannies on the nib, and the beauty of rubbing alcohol is that it dries VERY quickly through evaporation, leaving the nib mostly dry and reducing the potential to rust. Dried on ink will need more pressure than "fresh" ink, but be careful not to bend the nib ends.Once I've gotten off as much of the ink as I can I just let the nib and pen holder sit on some paper towel for a while so that they can dry further before I store them away.
Some nibs have attached reservoirs on them, especially if you're using the Speedball brand nibs that come in the variety packs at the local art/craft stores. These can be a little annoying when trying to clean your nibs as the reservoir creates a space where ink can get trapped, allowing it to dry and gunk up the nib. Personally I've found these reservoirs more trouble than they are worth as I find that not only are they difficult to clean but, for me, they also load to much ink on to the pen when writing. I've ripped the reservoirs off when ever they've been attached to a nib that I use. This is where the pipette comes in handy, use it to flush the rubbing alcohol under the reservoir. Another option is to try to side some paper towel between the nib and reservoir, be careful as you do this though as you don't want to pull the reservoir to far off the surface of the nib.
You will need a whetstone, I bought mine from John Neal Booksellers - Hard Arkansas Stone.
My first step is to put a drop or two of water on the end of the whetstone and just rub it into the stone a little, I'm not 100% sure if it's actually needed but all the things I've seen and read tell you to moisten the stone with either oil or water.
|Step 1: Sharpen the very tip of the nib.|
|Step 2: Smooth the edges of the nib of any burrs.|
Step 2: I will then turn the nib so that the side of the nib is resting on the edge of the whetstone. Again, moving from the shoulder, stroke back and forth a few times to remove any burrs. Repeat this for the second edge.
|Step 3: Smooth the back of the nib at a very slight angle.|
|Step 4: Sharpen the front of the nib.|
Step 4: The last step with the whetstone sees me working the front of the nib. Lay the nib on the stone and then angle it up to about a 30% angle, use the back and forth motion a few times.
If you look closely (use a magnifier if you like) you will see bright clean metal around the areas the nib has brushed against the whetstone.
My very last step is to run the edges over the leather whetstone sleeve to soften them off a little.
It's important to remember that although you're "sharpening" you nib, you don't want it so sharp that it actually cuts the surface (paper, parchment, etc.) you'll be writing on. Once you've tuned-up your nib try writing with it, if it's catching on the surface you can dull the very tip a little by going back and repeating step one with a couple of strokes.
My habit is to tune-up my nib at the beginning of my scribal session. On occasion, if the piece I am writing is really long, I will need to pause part way through to give another quick tune-up. Once you've done this a time or two, you'll get a feel for how much or how little you need to tune-up your nibs. It's not difficult to do and it will not only prolong the life of your nibs a little but also help the nib move a little easier across the page.
 Don't use oil on the stone your using with your nibs as you don't want that transferring to your finished page.
Sources & Bibliography:
Class taught by Eva Woderose at Known World Herald & Scribes Symposium in CT, 2012.
Other various sources of which I don't remember.
BROWN, Michelle P. & Patricia Lovett. The Historical Source Book for Scribes. London: The British Library, 1999. Print. ISBN 0-8020-4720-3