I am wanting to build a project which will use an op-amp which requires a positive and negative supply.
I am planning to build a power supply for this, using a small transformer and a circuit like the one shown here
Is there a better, easier, or more modern way to accomplish a negative dc supply ?
That's as good a way as any. There are fancier ways of doing it, especially if you only have a single supply but what you show is a good starter. You will of course need a transformer which has a centre tapped winding, something like 12-0-12 volts.
Looks like a good supply schematic ( you may want to add a 5 volt regulator).
You need something that can deliver a decent current in experiments so I would go with it. (or buy a ready made one)
What is your transformer voltage? Is it center tapped?