This is a great question. A comprehensive answer would be beyond the scope of an answer on a forum like this. I will summarize the best I can here, but if you are really interested in this you should look at some of the work by Randy Schekman and Tom Rapoport, who have done a lot of pioneering work in this field and have papers from more than two decades ago on their lab websites. I'll talk about membrane proteins generally, but I'm not sure what the state of the field is for Na+ channels specifically, so I can't comment too much on that particular case. Many of the details of the processes I will mention are still areas of active research, so I will try to stick mainly to what has been well-characterized (to the best of my knowledge).
To restate the problem, proteins are generally synthesized in the lumen of the endoplasmic reticulum, which is an aqueous environment similar to the cytosol in many (but not all) ways. However, membrane proteins, which are not stable in aqueous environments, must:
1) Find a way from the ER lumen into a membrane.
2) Get from the ER into the correct membrane so they may perform their cellular function.
We will start with step 1, but the key to both is a critical but often underappreciated aspect of protein biology called the signal peptide. The signal peptide is simply an N-terminal sequence of amino acids that precedes what we would normally think of as the beginning of a mature protein. It is relatively short, usually only ~30 amino acids in length. It is cleaved off the mature protein by a protease once the protein is folded and in the membrane. Until that time, the signal peptide serves as a molecular marker that indicates where the nascent protein should be heading and how it should be handled. Not surprisingly, there are many different signal peptides that serve multiple functions, and they are not only used for membrane proteins.
So let's say we are in the ER lumen, and have some mRNA coding for a membrane protein that is destined for the plasma membrane. The first amino acids that will emerge from the ribosome is the signal sequence, in this case a specific signal sequence indicating that this is to be a plasma membrane protein. Once the signal sequence emerges from the ribosome, it is recognized by a ribonucleoprotein complex (that is, a complex of RNA and protein) called the signal recognition particle. Once the SRP binds to the signal peptide, translation is halted, and the whole complex moves to the ER membrane, where it forms a complex with another large protein complex called the translocon. I can't go into the intricacies of these complexes and their functions in this answer alone, but the simple description is that the translocon contains an ATPase that can insert the membrane protein into the ER membrane as it is translated, with the correct orientation. The hydrolysis of ATP provides energy to move the emerging polypeptide chain into the hydrophobic membrane, where chaperones help it fold. This process is in part driven by the recognition of hydrophobic transmembrane regions of the proteins by the translocon. It can also move soluble, cytosolic proteins across the membrane through a similar mechanism.
Now that the protein has been translocated, a peptidase will cleave the signal sequence off the protein. From here, sorting signals will take over. Generally, these are simple sequence motifs in the first transmembrane domain that act similarly to a signal sequence, but they are not cleaved. However, sorting signals can be stretches of peptide throughout the protein too, in some cases.
These sequence motifs will be recognized by cell trafficking machinery. Without going into too much detail, the proteins will be gathered into vesicles, and transported to other organelles. Usually, the first stop for proteins is the golgi apparatus, which is typically where many post-translational modifications, such as glycosylation, take place. I am a biochemist and not a cell biologist, so I am not the most qualified to go into the details of subcellular trafficking. Suffice it to say, once the protein is finished being processed in the golgi, it will be trafficked into other organelles, such as the plasma membrane using vesicle transport as before. From my understanding, the protein will be sorted into the proper vesicles based on its sorting signals, as well as other markers (in some cases, certain post-translational modifications on certain proteins can influence its trafficking). The vesicles recognize the proper destination membrane in part by the lipid composition of that membrane. For example, phosphoinositides have extensive influence on membrane trafficking, and many membranes can be differentiated by their phosphoinositide signature.
Anyway, that is a very broad overview of the answer to your question. I'm sorry I can't comment too much on the intricacies of cellular trafficking, I don't quite have the expertise to go through that literature quickly enough to answer your question in a reasonable time frame. I hope this is helpful in pointing you in the right direction, and good luck!