Joe921,
It's not usually possible to track and entire flight as many of the ARTCC frequencies are not yet covered by LiveAtc,
especially if it is a very long flight. You can often track some flights between major airports if they are within a few hundred
miles of each other, i. e. Boston, New York, Philadelphia, and Washington. This may be true of the West Coast also, Los
Angeles, San Francisco, etc.
One way to do this is to carefully listen to departure for the hand off to the center and what frequency they give to
the aircraft. You could then type in the frequency on LiveATC's home page frequency search box and see if LiveATC covers it.
Another way is to type in (for example) "zbw" in the airport search box. This will show all the Boston Center frequencies LiveATC covers. You may find the Center frequency there. (Thanks to Dave for providing all the Boston Center frequencies)
If you live close to a metropolitan area you should get an aircraft scanner if you don't have one. This will give you
some additional tracking capability, at least for maybe 100 miles for aircraft, depending on your location, altitude of
aircraft, etc.
You will want to check regularly for any added Center frequencies since they are being added to LiveATC regularly.
Happy listenting.