The colonist can pick the apples from the trees, but after a few days, the apples will fall onto the ground and roll around a bit, these are counted as rotten apples, so can't be picked up. Instead, they may or may not spawn another tree where they land, so the trees will naturally spread like real-life trees!
Alternatively, you can choose to chop them down for wood. You'll need to craft a lumber axe first, so don't waste all your starting wood on nice floor tiles otherwise you won't have enough to make a lumber axe.
All axes wear over time too, so will need replacing. I'll be adding other types of trees too.