The old tale of Fades turning sideways and vanishing is mostly true, as we know. They have the ability to walk into shadows and reappear in a different shadow on the other side of the world, almost instantly. Now Aginor, there creator, put over a hundred of them to there deaths trying to find out how they did it. But I think that the way this works is relatively simple... well on the surface at least.

I thought at first that somehow the myrddraal where using tel'aran'rhiod to move around, but then dream walkers would find them and it wouldn't be a mystery. However I believe that in a manner they use the Ways to travel. Now I know what you're thinking, Machin Shin would kill them and it would be a stupid method but I don't mean they use the ways, but the space around them:

"As thought the opening stood alone with nothing around or behind it but the dark. He said as much with a shaky laugh but Loial took him seriously. “You could walk all the way round it, and you would not see a thing from the other side. I would not advise it, though. The books aren't very clear about what lies behind the Way gates. I think you could become lost there, and never find your way out."

EOTW p667 c44 “The dark Along The Ways”

The way gates are grown with only part of them in this world, but the rest is grown in a vacuole and this is where the myrddraal go (time for the major quote now):

“Abruptly the hand in her hair rushed her forwards, and she screamed in spite of herself. The Myrddraal meant to run her into the wall. Her hands went up for protection, and Shaidar Haran released her. She staggered at least ten steps – but her cell was not ten paces corner to corner..............

“Did you enjoy your time in the vacuole?” Moghedien felt icy fingers dig into her scalp. She was no researcher or maker but she knew that word. She did not even think to ask how a young man of this time did too. Sometimes there were bubbles in the pattern, though some like Mesaana thought that was to simple an explanation. Vacuoles could be entered if you knew how, and manipulated much like the rest of the world – researchers had often done great experiments in vacuoles, so she vaguly remembered hearing – but they were outside the pattern really, and sometimes they closed up or perhaps drifted away. Even Mesaana could not say what happened – except that anything in them at the time was gone forever.”

COS p461 c 25 “Mindtrap”

I believe that these vacuoles are the gaps in the between the pattern threads were the ways were grown, after all the ways could have been the research done, and it is possible that the myrddraal can enter these spaces and reappear in another just like if they used the ways, but it would be much faster as time and space would be irrelevant in a void.

As a side note to this theory it might also be possible that these vacuoles are were skimming takes place, the conditions are the same i.e. endless darkness

“Skimming, a process similar to travelling was occasionally used by those less adept. This method involved the use of platforms or steps in the void outside the pattern to carry a traveller from one point to another”

Quote from the BWB.

However this is idle speculation, my main theory is that the myrddraal use vacuoles to travel which are the spaces outside the pattern, where the Ways were grown.