For a simple OPAMP where I provide a + and - power input, how can I tell how much current these lines will draw?
The current drawn from the supplies is the sum of the device's quiescent (not doing anything) draw, which is specified in the data sheet, and the current drawn by the load.
Load current is simply the maximum amplitude of the output across the load. It's probably easiest to assume that, for power draw reasons, your output will always swing to the op-amp's maximum output, even if it rarely does. Or you could pick your circuit's maximum output voltage and use that.
Remember the load includes both the thing you're driving with the amplifier and the op-amp's feedback network. (In an inverting amplifier, the feedback resistor connects to virtual ground, so the current in that resistor is easy to calculate.) That is, the load impedance and the feedback resistance are in parallel. The load resistance may well dominate so you might be able to ignore the feedback resistance: a 1k load impedance swamps a 100k feedback.
If you assume AC signals that swing equally about 0 V, the draw from the VCC and VEE rails will be basically equal.