The previous poster is correct - you want to paint the ends as soon as you can with a sealent - either anchorseal or a thinned down latex paint, glue, etc. This is to drastically slow down the drying process through the endgrain. Don't worry about the sides - they will be fine.
As for cutting up the wood, you have to choose what you want to do as far as turning it wet or dry. If you want to turn it while it is still green, leave the piece whole until you are ready to turn a piece or two - this will keep more moisture in. If you want to turn it after it has dried, then you can cut it into sections, apply sealent to the endgrain, and place the wood in such a way that air can circulate around each piece. Keep in mind that unless you use some artificial means of drying the wood such as a kiln, the wood will take about 1 year per inch of thickness to dry.
Personally I like to turn the wood while it is green into roughed-out shapes, approximating what I want for each piece's final design, but leaving about a one inch wall thickness for bowls and the like. After rough turning I use the wet shavings as insulation for the bowl as it is placed in a real paper bag (not plastic). Check the shavings once a week or so for a few weeks spritzing them with water and placing the shavings and the bowl in a dry paper bag. This allows the moisture to come out of the bowl fairly evenly which hopefully will prevent cracking. After a few weeks of this you should be able to take the bowl out and set in in a well ventilated place where the temperature and humidity stays fairly constant, and let the pieces dried for 3-6 months. Once dry you re-mount the wood and turn it round once more, then complete the piece.
Hope some of this helps -
"Keep those shavings flying!"