First, I want to be clear, that there is no universally fair way to elect a president. All methods have pros and cons, and you can have your own opinion about which way is the best.
Right now with the exception of Nebraska and Maine, the electoral college is decided by whoever has the most support in a state. The winner usually has a majority of votes, but sometimes no single candidate was a majority. This method also helps smaller states as they have a lower ratio of voters to electors than larger states.
This method makes it easy to determine the winner on election night. You don’t necessarily need all the votes to come in if you have enough information to predict the winner.
Most states have a clear winner party. So most of the attention goes to swing states who do not have a regular winner.
The popular vote method is based on the winner of the popular vote. Whoever gets the most votes wins. This method can be implemented if enough states change their laws to award their electors to the popular vote winner.
Every vote counts the same. Larger states would have more power than the current system.
Smaller states lose some electoral power compared to the current system.
Congressional District System
This system awards 2 electors to the state winner and 1 elector to the winner of every congressional district. This is the method Maine and Nebraska use.
Disclaimer: This is my personally prefered system.
It’s a compromise between the current system and the popular vote system. The electoral college would probably mimic the congressional makeup.
Like the current system, could elect a president that didn’t win the popular vote.
All of these systems have pros and cons. There isn’t necessarily a “best” way to pick the president.
Here is a Five Thirty Eight article about different methods of deciding the electoral college.