If you've done it right then you've mentally driven the course before you even got to the starting line. Think about how you'll steer, where you'll brake, where you'll want to be back on the gas, areas where you really can haul the mail, and what your car's track position will be. All should be considered in your mind before you ever entertain driving any autocross course. Remember that this is your first time on this particular course and my recommendation is to continue that "get to know you" relationship. You'll almost never turn your fastest autocross lap on your very first run so use this to your advantage. Use this first run to identify that key apex to turn cones we talked about earlier and focus on looking ahead-far ahead if the course allows it. That Zen-like feeling I spoke of earlier? Well, it comes from your core or, in this case, your butt, as you feel where the car is at the moment, where it's going, and what it's going to do when you apply some steering, throttle, or braking input. You're not visually looking at where the car is at the present but where it will be many seconds from now. Keep those eyes up and moving; this is an acquired talent and one that all proficient autocrossers possess. Trust me and work hard on this part.
After The Action
You got around the course and crossed the finish line. Now you can breathe. Your time flashes on the digital display as you stop to get your official time slip before motoring back to the grid area. Most newbies worry about getting lost, going too slow, and hitting cones. If you've walked the course and are keeping those eyes up, you won't get lost. If you are confident about the elements and how to tie them together, you won't be slow. And if things don't go as planned, yes, you may annihilate a few cones. When presented with the choice of an orange traffic cone or going off course, nail that sucker and forget about it. Regroup, reacquire the course, and then continue at racing speeds to the finish. Each cone displaced from its box will add a second or two to your time. And if you take nothing else away from this, remember that you can never go back and redo time. Once you've hit that cone, that moment is history. Work toward the future and don't dwell on the past. A killed cone is just that: in the past.
One of the key things I do when back in grid is review my run. Hopefully, each run will be faster than the one before it and usually my final attempt on course is my quickest. This can be good or bad because, if I do push the envelope and get greedy, my final time may be my best but also may have a cone penalty attached to it, which really sucks!
My review is simple and I identify the areas, or elements, of the course that felt good and focus on those parts that weren't that stellar. Can I get further into that sweeper or accelerate out earlier? Can I get a little closer to each slalom cone? Are my braking points correct and am I braking in a straight line and to the threshold point? How does the car feel and can I be smoother striving for better balance? Simple stuff like that. I don't worry about the areas of the course that felt good. It's those sections where time was left on the table that are mentally replayed and addressed. Each subsequent run has fewer and fewer issues and after three or four runs, my time, give or take a tenth, is pretty much where it will stay no matter how many runs I take after that.