Where I can find a basis for connecting a GMR GF708AMA-AE sensor or someone knows a way to build or buy a suitable connector for this sensor. The path connecting surface is, and because of their small dimensions as the instrumentation is very difficult thereof.

 

I think you need to design a PCB to solder it so you can connect wires.

 

I guess you have two choices, either make a proper pcb and reflow it, or glue it to the pcb dead bug style use a microscope and solder on teeny tiny wires.
Or choice #3, buy the chip in a package that you can actually solder by yourself, like the SIL6 that has nice 1.27 mm pin pitch instead of 0.5 mm.