How can I determine if my outlets can easily be grounded?
Depending on how old the building is, and when the wiring was done. You might be hosed, or really lucky.  To find out which, you'll have to open up the box. 

Start by turning off the breaker to the receptacle in question, and verify power is off with either a voltage tester or a non-contact type tester.  Remove the receptacle cover, and undo the screws holding the receptacle in the box. Pull the receptacle out as far as you can, without damaging or disconnecting the wires from the receptacle.  If there is a bare copper wire hanging around inside the box, you just hit the jackpot!  Go out and buy a new receptacle (with ground), and hook it up.

If there is no ground wire in the box, You're basically done.  There was a time when you could use the metal shielding of Type AC cable as a ground (if the building was wired with shielded cable), but I believe this is no longer acceptable in the eyes of the NEC. 

Depending on the code adopted in your area, you may be able to replace the 2-prong outlets with GFCI receptacles.  If you do this, you'll have to make sure you label the receptacles "No Equipment Ground" (a sticker should be included with the receptacle). 

The best option at this point would be to call in an electrician, and have the circuits upgraded, or a new grounded circuit installed.