For size, the industry standard is in the range of L+W+H = < 62 inches each. (Although, I've never seen a ticket agent whip out a tape measure.) Your airline should be able to tell you over the phone, or their website may even have the information.
For anyone bringing boxes, I found the following to be really helpful: I tied twine around each of the boxes and made a big knotted bow at the top. I think it re-enforces the "keep upright" arrows, and it makes the boxes easier to handle, so that they don't get the old heave-ho out of the plane. However, if your boxes are really heavy, you should reinforce the edges of the cardboard that come into contact with the twine, otherwise you may end up having the twine cut through the boxes a bit.