Creating direct current (D.C.) increase voltage or current
Increase the number of turns of the wire
If you want to increase the voltage (and therefore the current) generated by the turning handle you can increase the length of the wire affected by the magnets. You do this by forming a many coiled armature. The small voltage from each circle will add together to give a much larger voltage. A coil with 100 turns will have a hundred times more voltage than a one turn coil.
Increase the strength of the magnet
Increasing the strength of the magnet will produce a stronger magnetic force on the wire and therefore more voltage (and therefore current). But that is not always easy. A bigger magnet helps but you can also make better magnets. Better magnets can be made using expensive alloys or expensive manufacturing processes and there are thousands of ways scientists are trying to improve them.
Increase how fast you turn the handle
The faster you turn the handle the more voltage (and therefore current) will be generated. The problem is that the more current you generate the harder it is to turn the handle. Because electricity is now passing through the coil, the coil itself is now producing a magnetic effect and Lenzs law says that it will try and oppose this movement. The faster you go the harder it is to turn. This is why, when you need large voltages or current you need a very powerful turning handle.
Powerful turning handles come in many forms but a major form you will be familiar with is wind turbines.
Slow moving but powerful blades have enough force to move very high ratio gear transmissions to generate fast turning spindle shafts to generate electricity.