Hi Joumana,
I have done a couple of different coptic bindings (it is my favorite, too) and I have learned them from Keith Smith's "NonAdhesive Binding III - Exposed Spine Sewings". I am a visual learner so the verbal description was not as much help to me. Taken together the text and the drawings eventually clicked.
I'm afraid a description could be long and possibly wouldn't be terribly accurate since I don't always use the accepted terms. I would hate to lead you off of the right path with my special brand of beginner wisdom.
In my album here there are photos of 2 books. The book with the Native Americans and the arrowhead on the cover is sewn through each set of holes only once. The larger, black journal is sewn going into each set of holes twice. Each uses one string per 2 holes, or sewing station, with a needle on each end. Each formed a subtly different pattern. Both are beginner efforts and not as well-photographed as I would like.
Sorry I can't be of more help than to recommend a book but I guess that's what we're all here for - to pitch in where we are able and to absorb whatever anyone else throws out there if we can.
I look forward to seeing some of your efforts.
Cheers! - Khajha

Hmm. I may be misunderstanding the question...I too have limited experience with these, and don't have any books on hand that describe it properly. But the way I'm used to doing these *does* require you to go into each hole with one needle, then out of it with the other. The last signature has an extra loop of thread through it as well. The Frosts strongly recommended notching the spine at the sewing stations instead of merely piercing it to facilitate this.

Verbal descriptions are always inadequate, but here goes:

If you have no covers, start in the first signature with a thread with a needle on either end, bring one needle from the inside of the sig out through each of the two holes (you can do any even number of holes, but you need a thread with two needles for each pair of holes). Add the second sig, and bring the two needles in at their sewing stations. Inside the book, take the needle which entered at station A, bring it to station B and pull it out, while the one which entered at station B comes out at station A. Take each needle and make a kettle stitch (or chain stitch - I'm not sure of the distinction, and I've been told both words for the same thing) by looping the needle around the thread connecting sig 1 to sig 2, then bring each needle up to enter sig 3, and repeat the process. The final sig, you do everything the same, but end up instead of kettle-stitch-and-on-to-the-next, you go back into that final sig, tie the ends of the thread together and cut off and fray the ends.

If you have covers, then you still start inside sig 1, bring both needles out, and then enter the first cover, lace into the cover following your preferred pattern, come back out of the cover straight into sig 2, cross over inside and continue the kettle-stitch pattern. At the end sig, come out of the sig as usual, do your kettle stitch, lace into the cover, then return into the last sig and tie off as usual.

Um... did that help? Was it clear? The only other thing to make it look nice (that I can think of right now) is to make sure you do all your kettle stitches the same direction in a given sewing station. And of course try to keep a reasonably even tension on everything.