Is it possible to hookup two ultrasonic sensors to one Arduino Uno unit?
Yes, it is certainly possible.  There are a few things you need to be aware of:

1)  The Arduino UNO is 5V by design.  Many sensors (not all, but many) are 3.3V devices.  So connecting them to a 5V pin could damage them.  Since you seem to be just starting out, I'd recommend sticking with 5V tolerant sensors.

2)  The Arduino UNO only has so many pins available....obviously.  Different sensors require different amount of pins to 'work'.  For example, a temperature sensor might work with the SPI interface.  Another sensor might require 8 pins.  So if you start running out of pins, you need to think about other challenges like using shift registers, multiplexers, etc.

3)  Don't be afraid to experiment.  I suggest buying a genuine Arduino UNO to support the project.  Maybe buy some cheap Chinese ones to experiment on...in case you fry on of those.  

In theory, the sky's the limit when it comes to "how many".  In real life, if you start going over a handful, dozen, etc. then you might want to rethink your design.