congrats on the new purchase.
Think of it like driving a tank; the left stick controls the left wheel only, & the same for the right.
Put your coordination together & go for it. Could take it to a parking lot & practice keeping front tires on the lines for straightness practice.
Also do a search on tires tearing up turf. When you do a zero turn the inside wheel that is sitting still needs to be moving backwards so it doesn't tear up the grass. Practice on your own lawn & watch the grass after each turn around until you don't tear it up anymore. Just remember to keep both wheels movin'. I have ATV tires on my 25 hp/61" bobcat, & I REALLY have to keep them moving.
Once you get used to the ZTR, you will hate mowing with a steering wheeled mower. Like going back to a dinasaur after flying in a jet. As Smitty mentioned, keep the wheels moving. When you back up, pull both levers back before making a turn while backing. If you pull just one, it may spin. Once you get it moving back, then start your turn. ZTR's are the only way to mow. It will mow twice as much or more than anything with a steering wheel of the same width. I have some striping tips on my Website it that will help you at all. Good luck and Congrats on the new equipment.