I have just started building circuits last year and mostly stripboards, so these are still things that I don't know: where do you connect the points marked by red underlines and green half circles in this schematic?

 

where do you connect the points marked by red underlines and green half circles in this schematic?

The symbols marked with red represent circuit ground. Technically it represents earth ground. Circuit ground is represented by a triangle outline. They and the 2 +15V symbols are what are referred to as connect-by-name; they simplify schematics.

The +15V, -15V, and ground are power supply connections.

 

My power supply connects like this. Note the Green Wire (ground) connects the (+) and the (-) together.
Do not use the "GND" on this supply.

 

The +15 and -15 are power supply points. The operational amplifier uses a dual supply, a + and - supply. I see ron already provided an image so I won't say anymore.

Ron

 

That schematic requires a power supply with three output posts, -15V, +15V, and ground.
[too slow!]

Depending on what you're doing, this circuit might work with two 9V batteries connected in series. "Ground" would be where the two batteries connect. Or two 12V batteries.

 

You need a power supply that has three connections:
+15 V
COM or GND
-15 V

(±9 to ±15 V will work)

 

Or two 15V power supplies with isolated outputs connected in series as in post #3.

 

It is best practice if the schematic of a circuit is uncluttered and clear to read.

It's a common practice to take power and ground points and label them as such rather than draw wires connecting them. For the purpose of wiring the circuit all such equivalently labelled points should be connected together.