How to Transfer your Homeworld.
Short version:
If you have no characters it is free. If you have characters it can be expensive.
Try to switch during peak hours, Friday after noon is the best possible time.
Still very random.
Buy the gems you need in advance. I had 2600 ready but I only needed about 1800.
Log in, click transfer or chose homeworld, sort by population.
If it is not full, transfer, good job.
If it is full then log out completely and check back in about 30 minutes. (Or less if you are super bored and not doing anything).
This could take 1 try, could take you over a week.
Hope and pray to the gods.
Long Version/Explanation:
I just yesterday managed to switch to Tarnished Coast which has been a popular server for months or years. It is the 3rd highest WvW server and hard to get into.
Do not try during off hours. For the server to drop below full people need to transfer out. It does not matter if no one is playing. In fact you want to try during peak hours because then there are a lot of people who might be transfering.
If you have any characters it will cost gems to transfer, it cost me 1800 (or about, can't remember exactly). Which is expensive but I had a lot of characters high levels. If you delete all of your characters it is free. You will keep everything in your bank and material storage.
Fridays are the best days to try and switch. The World versus World leaderboard resets on Fridays around 6pm PST. Many people try and plan their transfers around this time.
Despite all of that, it is still extremely random, you might get in at 1am on Christmas day, super random.
Have your gems ready in advance, log into GW2, click transfer, then sort the list by population. This way you will know immediatly if the server is not full because it will no longer be one of the first 5 servers. If it is not full scroll down and find it and transfer. If it is full log out completely and check back in 30 minutes. Expect this to take a long time, possible weeks. You might get lucky and do it on your first go though. It took me 3 days of actively trying to switch though I had been checking every day for months.