Hey, this was just me a few months ago - until I had some awesome help from the forum & a friend. Having a neatly pulled mane is so much better than using scissors on it - previous mistake I made. Ek!
Never leave your mane dirty - some people say it makes it easier to braid, however it looks messy & you will loose points in presentation classes. Although shampooing your horses mane a few days before you braid it is much easier than braiding it the same day - its less "slippery". Also - braiding the mane/plaiting always seems to have these little "fray like" bits after your done.. however - this can be solved! Eggwhites, using them to "glue" the hair/mane down is amazing.
I agree with above posters. Pulling TIGHT and trying to keep them flat will help greatly. Other than that just practice practice practice. I haven't braided in quite a long time but when I did I would always take lots of pictures of my job and compare them. It was good motivation to keep trying to improve!