I'll tell you from what I have learned over the years of training barrel horses is that I push with my inside leg (the leg next to the barrel) then I keep kicking with my outside leg, also when I turn my horse around the barrel I pull his head or nose to where it is almost touching the barrel. I hope this helps.
It is hard to give you tips if you haven't started yet.
What I advise you to do is to listen to your trainer and read a lot about the discipline before.
Here is a website I like with a lot of different tips about barrel racing : http://www.freebarrelracingtips.com