How to write horizontally across the blackboard while keeping handwriting as horizontal as possible?
Writing works different on different heights, so train writing at different heights. For me it is easiest to write horizontally if the baseline is about the height of my  mouth. Writing at the height of my stomach or my chest is almost impossible and I need much more care and it takes much longer. If you have to write at that heights, you could also squat down, but be aware that the things you write down there may be too low for some people in the audience.
If you can move the blackboard up and down, move the blackboard such that the line you write is on your favorite height.
Do not stand still and stretch your arm more and more, but move your whole body along as you write.
Related to the previous point: Use short lines. Two halves at a ten meter blackboard still make five meter long lines. Depending on the size of your writing, this may still be too long.
Try to get good chalk. I prefer chalk that slides over the board more easily. (The people over at mathoverflow have something to say about this, see here and here).
Try to adjust your font such that it helps you to stay on the line. Writing cursive for text (not equations) may work, but I think cursive needs more care on the blackboard.
If you practice, try to find a blackboard that has lines, a grid or crosses that help you stay in line.