You'll have mains electricity only up to the terminals of the transformer. You isolate those with electricians tape, heatshrink, whatever.
The outputs of the transformer 24v ac, or +15v , -15v etc are all floating. It's also low voltage so it's not really a safety risk unless you put your tongue on it or something like that.
You just have to know that the metal back of the chip is connected to what would be -15v on your power supply. Traditionally, circuit boards are grounded to what they're screwed on (ex on motherboards ground in the connector coming from the psu is connected to the metal case through the screws sometimes) so if you do that and the metal heatsink touches the metal case you have a short circuit.
If you put the prototyping board and the heatsink in a plastic box (abs) the heatsink is basically not touching or shorting anything, so you don't need insulation. And if you touch it with your hand, at best you're going to feel some tingling in your fingers and the chip may reset or make awful noise (you're may short the -vs to ground through the big resistor your body forms)