Plant the seed in acidic soil in a pot, and keep warm and moist (but not too wet). They like hot humid climates in summer (30°C, high humidity), and a winter minimum of 10°C. They are quite easy to grow when young, as long as the air around them is not too dry.
If you have a greenhouse they should survive for years, as they need the humidity and relatively warm temps above 17C....
Yeah, it is a tropical fruit so it needs that extra warm temperature. Unless you live in a warm state or have a green house, you may have a hard time. But just like any other plant, make sure you use high nutrient soil that has some composting such as worm castings.
here they ar eabel to survive without any damage brief periods down to 5C that i have seen. brief= a day or night lows. but that is "not dieing" not "happy" like they said above, hot n humid wins the race.
my first attempt to germinate lychee seeds was just by simply placing the lychee pit in a piece of wet paper towel on a bowl with a piece of clingwrap on top. surprisingly it worked! but this may just be because I live in a warm and humid climate, but you could try, it won't harm.