There are two main approaches to doing cross stitch; the English cross stitch style, and the Danish approach.
Both approaches are described below but neither are correct, and neither are wrong. It is very much up to personal preference and what seems to make sense when you are following your counted cross stitch pattern.
The English Approach
An individual cross stitch is completely sewn before moving onto stitching the next cross stitch.
Start by stitching from one corner to the next corner. It does not matter which direction you do this, provided you use the same approach consistently. Below, the thread goes from top right to bottom left
Stay on the same column and go back to the top of the square on the reverse side of the fabric. In the following figure, the stitch direction on the front of the fabric for the second part of the cross stitch is top left to bottom right.
On the reverse of the fabric go to the top right of the second square, and stitch to the bottom left again.
Then follow the same pattern as for the first square, stay on the same column and go to the top of the square on the reverse of the fabric. And then repeat the stitch on the front of the fabric going from Top left to bottom right.
The Danish Approach
A row (or column) of half stitches are made. The cross stitch is completed by reversing back down the row using the symmetric pair of the cross stitch.
Start on the left making a series of half stitches.
When you have completed the required length of half stitches, reverse direction, heading right to left to make the crosses.
Please provide your comments about how you do your cross stitch - I think it is a very personal preference - but I would love to hear about other ways so that we can all learn from each other!