How can create a simple circuit that will drain a battery in a few hours
It'll just burn dimmer for longer that way.  What you need to do is pull more current out of it.   First I would get a cheap voltmeter you can probably find one for $15 or less.  Then if you look at this datasheet for an energizer AAA battery you'll see they have a discharge chart in there.



So if you want to kill a battery in less than 10 hours you'll need to suck out around 100mA of constant current.  Starting at 1.5V that would mean you'd need about a 15 Ohm resistor.  It'll need to be able to dissipate that power so P = 15Ohms * 100mA^2 is about 150mW of power.  So look for a 15 Ohm quater watt resistor.  As the voltage goes down so will the current draw but that should be fine for this experiment. Just take a voltage measurement every hour or after 10 hours, it's up to you to decide what voltage will mean it's "dead".  Don't just short the battery though that could be dangerous.

If you want to do the LED thing because it looks more exciting :)  You just need to pick a lower resistor value and maybe a higher power or more LEDs in parallel (with current limiting resistors).  The reason you blew the LED the first time was you pushed too much current through it, and the reason it didn't work with one Battery is because there's a voltage called the forward voltage for the LED that must be met before current will flow.  You can find it in the LED's datasheet along with the max current the LED can use and use that to calculate the lowest value of current limiting resistor you can use.

Here's another helpful chart for you to use from that datasheet.


That gives you and idea of what to expect will happen to the battery over temperature.