Pulling manes so that it is all the same length & thickness is an art - it is very difficult to get it all even if the mane naturally grows thicker & longer in places.
It is best if you can get someone to show/teach you (freelance groom or knowledgable YO) but the basics are:
run your hand down the bottom of the hairs of the mane, when you come to hairs that are longer than the rest, squeeze it between your fingers, back comb the other hairs in that area so they are out of the way, then wrap the bit you've still got in your fingers around a pulling comb & firmly pull out at the roots. You should only be pulling a few hairs at a time otherwise it will be painful for your horse.
Some horses like it, some don't - I personally always use a solo comb as I find it kinder. You do the same as above but instead of pulling the hairs out you cut them with the solo comb.