How are the golgi apparatus and endoplasmic reticulum related?

The ER and Golgi work together to facilitate the anterograde and retrograde transport of proteins. They are both parts of the Endomembrane system.

To put it briefly:

Anterograde transport: The Rough ER is the site of mRNA->protein protein synthesis, which is carried out by surface-attached ribosomes. A large number of these synthesized peptides have destination-determining sequences, and some are packaged into vesicles that fuse to form the cis-Golgi cisternae.

These vesicles can carry cargo that is packaged into lysosomes, transmembrane proteins, or secretory proteins, among other possible destinations.

Retrograde transport involves the fusion of golgi vesicles with the ER to contain external proteins that are meant for the ER.

Read more about: Signal recognition peptides (SRP) COP1 and COP2, Clathrin-coated vesicles and Lysosomal targeting, KDEL Sequences, Microsomes, Glycosylation in the ER, Co-translational translocation, Translocon, Sec61, TRAM.

Reputable references: Chapter 11 of Alberts Molecular Biology of the Cell, Fifth Edition.

Endoplasmic reticulum synthesizes proteins and lipids, which are subsequently modified and packaged into vesicles; these vesicles are transported to the Golgi apparatus, where additional modification and sorting takes place before the molecules are sent to their final destinations within or outside the cell. The Golgi apparatus and endoplasmic reticulum are related through their roles in the cellular secretory pathway.