Impossible to say with any accuracy, other than these general guidelines - once you've planted your seed into the growing medium, water it well. If the seed is very small, then get the growing medium nice and damp before you plant, but not too damp or the carboard tube will disintegrate. Then sow the seed into the damp compost. Check it daily, feel the top with your finger - if the cardboard looks damp or wet, don't water, if it looks dry and the compost feels dryish to the touch at the top, then water gently, sufficient to moisten but not to soak or wash the seed out. As the seedling starts to grow, follow the same watering routine. The rate at which the compost dries out will vary according to temperature and humidity levels, but having it too wet can cause damping off disease, which will likely kill your seedling. As the seedling grows, if it is a large tree, it will very soon need potting up into something larger, but without knowing what it is you're growing, impossible to say much more.
UPDATE: You've said you've lined the tube with plastic - I hope its not like a bag in that it's sealed at the bottom, you will need drainage, so make some holes in the bag if its not open at the bottom already. I'm very curious as to how you're expected keep your tubes upright in the meantime, and without water leaking where you don't want it.
UPDATE 2: A bean seed, well, not even remotely treelike then. keep the compost moist but not soaking - should germinate and need potting on within 9 days, they're rapid growers, although you've obviously not been told what variety of bean it is. I'm assuming its the runner bean type that kids get given to grow using blotting paper and a glass tube in school, so they can see root growth.
