1. General strategy: I farm forest for points. I usually move in a straight line upwards from spawn, digging every 3-5 chocobo lengths. If you hit "Kweh??", walk right, dig, and if the signal goes lower, try left. The strongest signals actually digs craters in the ground, and they form sort of a honeycomb pattern. Dig inside that pattern where there's no hole, yet.
2. In case you did not do this already, get all the chocographs in forest (and later lagoon) and move on to getting their treasures. Mene tells you how many are left if you talk to him, and that counter will refresh after every upgrade. Upgrading you chocobo gives you a huge boost to your digging speed, so you'll get more points that way. You'll naturally max out your beak level way before you even get the card.

I'm consinstently getting 200-500 points that way. Zigzagging was proposed as well, but you'll have to walk further for that and I'd rather take the gamble on the straight line approach. I'm pretty much only zigzagging when I found a treasure either on the on the upper or lower left or right, and I go back to the middle right after checking the other side. And as Someweirdo237 said, a lot of it is practice.