Hi. Good question.
This depends on the type of protein and where it functions. Cytoplasmic proteins (those that work in the cytoplasm, e.g. enzymes used in glycolysis) will fold into their correct conformation (shape) and either diffuse to their correct location or become packaged into vesicles for transport by motor proteins traveling on microtubules.
Proteins that are meant for the cell membrane, outside the cell (secreted), or for "extracellular" organelles, such as the lysosome or phagosome, must go through the endomembrane system, aka secretory pathway. These proteins will begin translation on the ribosome in the cytoplasm. Their amino acid sequence contains a specific sequence called the signal sequence (16-20 amino acids) that signals to the ribosome that this is a protein meant for the secretory pathway. The ribosome will then STOP translation and move to rough ER, where it will continue translation such that the protein falls into the lumen (inside space) of the RER. This protein will fold into its conformation and be packaged into transport vesicles and taken to the Golgi. The Golgi will then modify the protein (maybe add carbohydrate groups or fatty acid chains) and repackage it into transport vesicles. These transport vesicles will deliver the protein to its final destination (cell membrane, secreted by exocytosis, or lysosome).
Cytosolic proteins: protein folding --> stay there & function, or diffuse to correct spot
Secreted, membrane or lysosomal proteins: endomembrane system aka secretory pathway ==
ribosome in cytoplasm --> rough ER --> vesicle --> Golgi --> vesicle --> final destination