If you're playing the game unregistered, you are limited to 7 villagers and the technology levels that you currently have. Since every other puzzle requires higher levels of technology and/or more people in your village, the things you can do now are limited to keeping your villagers happy and healthy and responding to Island Events as they occur. As your villagers grow old and die, you'll be able to make baby villagers to replace them.

If you've registered the game, the best thing to do is to continue to research and take one of your adult villagers exploring every time you're able to purchase a new level of village tech. There will be new opportunities as your village grows and they discover new technologies to use in the village.