The AAA will only give you around 1.5 volts, and the LEDs need about 3.6 or so. This gives you two options...
1.) Buy a voltage step-up converter
2.) Use two or three cells, rather than just one
I would recommend you try option number two, unless you need the circuit to be small, in which case a voltage step-up converter would be necessary.
Because you do not have a lot of voltage, you should wire the LEDs in parallel. This way they use more current (amperage), rather than voltage.
When using two cells you can direct drive the LEDs, or use some resistorance. When using three cells I would definitely recommend you add some resistance to the circuit. For more information about resistance, and how much you need,
take a look here.
So basically your circuit is going to look something like this.
Image from
here.