Ooh ooooh.  Me first! (Raises hand and waves vigorously)

Good question Tango.  I know I may sound like a broken record, but, as with most things about snowboarding, it is personal preference.  Some folks will just know whether they are regular foot or goofy foot.  Those people will most likely have skateboarded, wakeboarded, or surfed before and just ride the snowboard the same way.  I suppose if you have ridden one of those kick scooters that were really trendy a few years back, it may have given you preference to putting one foot forward and one trailing.

If you have no previous [sideways] sports skills that might cross over into snowboarding, that's OK, there is still hope in choosing a directional preference.  Find a situation where it is really slippery.  It may be an icy spot on a frozen walkway or just on the kitchen tile in your socks.  Now run forward a little bit and slide.  Try to slide as far as you can.  You will find that you naturally will begin to lead with one foot when you do that -- and there you go.

Another way is to close your eyes and imagine snowboarding down a PERFECT run.  For me that would be a wide open powder field, well above tree line.  As I progress, the run gets a little steeper and I start to gain speed.  Now I can head to the right, slowly transition to the side, start slowly heading left as I progressively bank into the turn.  Speed increases.  My board starts to plane.  As the force presses me deeper and deeper into the snow, I can feel it flex my board from the pressure.  I hold strang in the stance as I head straight down the fall line and eventually cross over it slightly.  As the pressure has built to a maximum, I go for more speed.  I pull my legs in flatten the base and ramp out of the powder.  As I clear the snow surface, the momentum of my tipping carries my board behind me as im tipping toward the downhill.  Re-entering the powder I get the same sensation as before, but this time it's on the other side.  The fresh snow, the fresh air, the seclusion, the pressure, the release, the hill steepens, tiny frozen pines appear, left and right turns are nothing compared to the scope of the terrain itself.  In perspective it is a straight run.  In perspective it looks too steep, but to me it is just right.  Over my trailing shoulder I look behind me, and all I see is a roost of sparkling airborne powder, sometimes swirling in a vortex.  I catch a glimpse of more little trees and decide I better look forward again.  Back to looking over my front shoulder, I notice I'm now in a gladed meadow.  The only sound is my jacket and pants flapping; not from the wind but from the velocity.  Bank, bank.  Left, right, left, right...  Like a dolphin my board comes out and dives back in.

OK, I will stop there.  Read it over.  Make sure you get to where you share that sensation along with me.  Sweet!  I italicized one phrase in that text, "Back to looking over my front shoulder".  So is that looking over the right shoulder or the left?  I know what it is for me, do you know which one it is for you?

OK, if you are still stuck, don't worry, one way is not any harder than the other.  They are both hard, LOL.  Simply pick one orientation and stick with it.  Stick with it.  Stick with it.

Whichever way you choose, dont ask someone at the rental shop and let them push you!  (You know what I mean if it has happened to you)

Frosty has a great response! And definatly dont let them push you. They tried that on me
and I found I was catching my weight with which ever side of my body became off balance
1st. Not a good way to establish direction.

Someone told me once that they were asked which foot they would kick a ball with. That
seems to be a good way to figure things out as well.

Of course you might be in the low percent rate that can automatically ride switch.
If its really hard to figure out, rent a twin board and just ride both. It'll be set up one
way, but because the board is exactly the same on both sides it wont matter if
you spin it around. One way should feel wrong, one way should feel right.

My natural ride is goofy, but riding that way I find it hard to execture heelside turns well.
When I ride regular I can turn very well but when it comes to hitting jumps or taking rails,
its a bit awkward and I usually fall. So I switch it up when I get centered, or ride in at an angle
that I need to toe into.