Oh dear... as a non-English speaker by birth, but coming from where the cravats were invented, below is my contribution. Some terms may be wrong, but they are the best I can. I have my husband's cravat out to practice
1. Assuming that you'll need to do this a few times to get the final lengths of the two ends as you like them best, start by putting the scarf around the neck and having two ends of the scarf pointing down. Hold each end with the respective hand.
2. You'll do most of the work with the right end of the scarf, while the left ones are mostly still and keep things in place.
3. Take the right end and put it under the left one...
4. ...then over and back to where you started from (i.e. to the right side). Right now your right end of the scarf itself is pointing to the right.
5. It's probably a good idea to put the finger of your left hand at the part where two ends cross each other, as if to keep them in place (thumb underneath and another finger on top).
6. Top half of the scarf is now forming a loop around your neck.
7. Now take the right-end of the scarf, put it around the right top part of the loop...
8. ...and finally thread it through the new loop that had formed itself at the place which you are holding with your fingers to keep things in place (as described in step 5).
9. Tie the knot as firmly as you like.
I hope this makes sense.