I have some spots here that get a good amount of sun but a majority of this property is in the shade. Other than picking plants that are adjusted to that setting, what could I do to help with the sun problem?
Unless you can take down some trees or whatever else is obstructing the sun, not much. In the spots that get good sun, you can try to grow vertically, to give yourself space to grow a bit more. Some plants, like lettuce and such, can be grown indoors with artificial lighting.
bit hard to move the sun, you could put up some kind of reflective items, mirrors or whatever, to direct some sunlight in, but just finding plants that grow in that spot is probably a more sensible option. If it is dappled sunlight, you can still grow any number of veges that say you need full sun. The trick is picking varieties that handle the condition better. I grew some pumpkins last year and the vine took off into my fruit orchard and I ended up getting my best pumpkins in and under a huge cherry tree where there was almost no direct sunlight. I had 3 varieties of pumpkin and 2 were fine, the other suffered very badly with mildew, so with less sunlight, this would be much worse. I also find other plants such as celery grow well in half sun, it would appear that they don't dry out as quick and so stay sweeter for longer.
Best is just to experiment and see what results you get.