The transistor is there to control the actual current through the load. It is essentially a voltage-controlled current limiter, in this case. The voltage/current relationship depends on a lot of things, and there are usually plenty of curves in the datasheet that shows this.
The resistor at the bottom is there to convert a current to a voltage. Ohm's law. All the current through the load will also flow through the transistor and down through the resistor.
U=I*R, so it is a linear relationship. This resistor is a compromise between the ability of the resistor to dissipate heat, the amount of loss you can tolerate, the amount of current you want, etc.
The operational amplifier is connected in it's "magic" mode. For an ideal OP-amp, there are essentially only two rules, perhaps paraphrased here:
- No current flows in and out of the inputs.
- It makes sure that the voltages on its inputs are the same.
You control the voltage on one input, so it has no power to change that. It can however control the voltage on its negative input, by making sure that the right current flows through the transistor and the resistor to make the voltage at the resistor match the set voltage at the positive input. It does that by adjusting the voltage at its output.
Naturally, no OP-amp is ideal. In this case, you have to think about a few things, mainly the input and output voltages relative to the OP-amp supply voltages. It has to be able to set the voltage to something that makes the transistor pass the amount of current you need, and the inputs should preferably be kept a few volts away from the supply.
If you don't already know this, the OP-amp you have selected is probably a bad choice, and the project will be somewhat difficult. This OP-amp may be fast enough, but only if used under optimal conditions. This includes a compensation capacitor, because to reach the speed and flexibility, it is not internally compensated. Unless you are experienced, you will most likely end up with a lot of oscillations instead of a functioning circuit.