All translation begins in cytosol, by a cytosolic (free) ribosome. Remember, the rough endoplasmic reticulum is studded with ribosomes. A protein has a specific amino acid sequence that signals the ribosome where that protein needs to move. If that signal is reached during translation of the protein, this is called co-translational protein translocation (a mouthful, I know.) This typically pertains to proteins that are involved in cell membrane structure or proteins that need to be secreted. The ribosomes move to the RER with the incomplete protein, and feed it into the RER.

For proteins that stay inside the cell, they are shuttled to where they need to go because of the recognition of their targeting sequence. This is post-translational translocation. Specifically, for nuclear import (which is very selective), a special tag called a nuclear localization signal (NLS) is attached to the protein so it can pass through the nuclear pores.

Here’s a nice paper on this: https://www.ncbi.nlm.nih.gov/books/NBK26932/ “…histones, DNA and RNA polymerases, gene regulatory proteins, and RNA-processing proteins—are selectively imported into the nuclear compartment from the cytosol, where they are made.”

I’d love to answer any questions you may have! EDITS: Spelling, structure of paragraphs