I am learning some basic idea on using op-amp and other simple electronics by myself. I am trying to build up my first circuit for using opamp (TL084) by following some online examples. In the datasheet I found for the chosen opamp, it is said that it need the input voltage -12V to +12V and with operating current not more than 120mA. I don't have the right voltage supply for that opamp but I got a very old variable voltage and current power supply, it said it supports 0 to 20V DC, 0 to 1A current. So if I turn the current to 0A and increase the voltage slightly up to 10V, do you think this will work also. I only have 1 TL084 and I don't want to break it. The shipment is not cheap so I would like to confirm that with someone before I try it on.
The TL084 has a recommended supply range of \$\pm 5V\$ to \$\pm 15V\$, so if you intend to run a single-ended supply (i.e. the negative supply rail is ground) that means the supply must be between 10V and 30V.
There is no theoretical maximum current rating for the supply, only a minimum current rating; see this question for more details. If you intend to draw 120mA from the power supply, your supply must be capable of providing more than 120mA. Setting the power supply to 10V and 1A is perfectly fine. Running at 20V and 0.5A is perfectly fine. Running at 10V and 0A is not fine because you are below the minimum required current.
Note that op-amps only work as designed when the output and inputs are between the supply rail voltages; you will not be able to build an inverting amplifier with a single-ended supply unless you use a virtual ground. See here for more information.