How do I implement a DPDT-switch here using NPN/PNP instead?
If I read the question correctly - it's short on detail - you want to replace a mechanical polarity reversal switch with a transistorised version. In that case you could use a H-bridge, so called because the load (the motor in Figure 1) forms the crossbar of the four switches (the transistors all connected to the motor form the legs of the H).



Figure 1. H-bridge controlled by one input signal.

The circuit shown in Figure 1 adds the BC547 transistor to the usual configuration. This inverts the 'A' logic for the transistors on the left of the motor while 'A' goes directly to the right side.

This may be enough information to get you started. 

Just watch out if you are using a load supply voltage > 5 V and controlling it from a 3.3 V or 5 V micro. Current will flow out of the base of the top right BD140 and back towards A and through the protection diodes of the micro. This could destroy the output or the complete chip. Some reading up on high-side switching should give you further ideas.