An FPGA is a general purpose configurable logic device. Constructing an application generally requires a high level software tool. In many cases the software tools cost upwards of approximately $5000.00 per seat. There are sometimes limted versions that can be downloaded for free from the manufacturer.
You can build up applications from gates and primitive blocks like flip-flops. Many software packages have higher level blocks like shift registers and counters. Designs can be done with schematic entry, VHDL, or verilog.