There's many different designs. In your picture the yellow risers are connected to the semi-sub which will store the oil (in the legs I think) until offloaded by tanker. The risers are flexible and the buoyancy modules you can see give the risers that lazy S catenary which is important to absorb any movement from the floating semi-sub. All the other lines connected to the semi-sub are for anchorage. The flexible risers are connected to rigid oil pipelines via a short static riser section at the bottom right of your picture. The oil pipelines connect to the many satellite wells. At the right of your picture is a single point mooring system that a tanker will offload from also.

In my photo the FPSO takes the place of the semi-sub in your picture. The FPSO (Floating Production Storage Offloading) is a large vessel converted to a processing platform. The risers connect to the FPSO where some degree of processing will take place before the oil is stored and then periodically offloaded to tanker.

In this field (Åsgard) the oil is transported via tanker in this manner and gas is pumped south via a 700km, 42" subsea pipeline.