Japan and South Korea are not visited by cruisers that often (although they are visited) because they are not very accessible from the normal cruising routes. Something else you should get hold of is Cornell's book, World Cruising Routes which describes typical routes from point A to point B (ie how far, waypoints to use, best season to use, season to avoid due to storms). You would use this to plan how to get to Japan from Panama or San Francisco in one step or many steps depending on the circumstance.
As for how you enter a country, it varies a lot. Couple of examples from last year for us. First of all you need to go to port of entry (see Noonsite).
1. To enter Martinique (easiest of all) you take your dinghy to town and go to the Customs office, sit down at a computer and fill out a form. You save it and print and the local official signs one copy that you keep with you. Free and takes about 3 minutes.
2. To enter Grenada, you go to the Customs office which is on the town dock and fill out a form; then you go to Immigration office in the police station and fill out some more forms; then you go to the Port Captain's office (next to Customs) and fill out another form; then you go to Customs again and give them a copy of the Immigration form. Somewhere along the way you pay some money. Takes 45 minutes and cost something like $50 as I remember.
3. To enter the US (we are Canadians), call in by phone on arrival and give them a bunch of info and get a get clearance number; within 24 hours report to the local customs and border protection with everyone onboard to finish the administrivia and (perhaps) pay some money. In our case, this involved hiring a taxi for $15 each way. With the ride to the airport took about an hour and half; total cost to be determined because we likely will need to get a new cruising permit.
Also, note that you generally have to revisit at least some of these offices when you check out of the country. US and Canada are exceptions to this rule. In many countries in Latin America you have to check into and out of each harbor you visit. In some places you cannot look after the formalities yourself and have to pay for an agent. The formalities vary and range from easy to incredibly complex, but you learn as you go and it is generally not too hard to do. We are investigating visiting China in 2112 but it is very complex as they have no procedures for visiting yachts (except in a few yacht races). You are treated as a ship and it is very costly (shipping agents, pilots, etc).
Start your research at the beginning, it will make sense as you go.
Finished the circumnavigation in early February in Grenada. Have to work on a book project for the next several months so the boat will be waiting for next year.