Good luck with your learning curve. You'll be on the steep section for a while. Here are several suggestions since I'm no where near you:
1. Find out as soon as you can whether your employer got the license(s) and paid for Subscription support. If not, strongly suggest that they get on this plan. It will assure you of access to help and updates and keep you current going forward. Next year's version (2013, we're current now with AutoCAD 2012) will likely be the tri-ennial Major upgrade. File formats will change and other changes in the program will be more substantial than what we see in the intermediate years.
2. Break open your own moth-lined wallet and get some good reference materials to work with during those times your tutor isn't nearby. Purchase only authorized Autodesk materials. Here are three I'd recommend that will serve you well:
"Mastering AutoCAD 2011 and AutoCAD LT 2011", by George Omura. Pub by Sybex.
"AutoCAD Secrets Every User Should Know", by Dan Abbot. Pub by Sybex.
"Illustrated AutoCAD 2011 Quick Reference", by Ralph Grabowski. Pub by Autodesk Press.
Or look for the 2012 versions of the above if you are on subscription and will be upgrading shortly. These will be invaluable deskside as you get back up to speed.
Good luck!
Dave.