The current is dependent on the resistance of your load, and the equivalent series resistance (ESR) of the capacitor.
Ceramic capacitors have very low ESR and thus can generate very high current. Electrolytic capacitors, however, have very high ESRs -- an ohm or more! -- and thus won't be very good at generating very high currents.
Also, as the current is driven by the capacitor, the voltage across it drops (because the charge dissipates) and thus the current will follow an exponential decay curve.
There are plenty of good references about capacitors, current, and charge (and Ohm's law, and differential equations, and inductors) on the web -- you probably want to find one or two and read through them until you understand them and can do the math that they describe on your own. Electronics is 50% math...