One of the many problems beginning players can have when trying to play a new race is that they fall back on stereotype, or worse yet, simply play that race as a human with some slight, cosmetic physical differences. An elf is much more than a graceful human with pointy ears, yet often players will treat them as just that, going for the looks and ethereal air without actually considering what such a being would be like. How can you help a player get into the mindset of an elf, and enjoy playing something truly different and inhuman?
First, you should strive to emphasize what immortality or a supremely long life does to a person's outlook. Elves are generally portrayed as immortal or living for countless centuries, and this longevity has a decided effect on their outlook on life. Gone is the urgency that humans feel, the need to do everything now, today. Instead, elves will prone to taking the long view, to considering ramifications to their actions that extend beyond the here and now. They will tend to be more philosophical, contemplative, to spend time admiring simply being alive, nature and the world, and less interested in acquiring money, power, fame, all things which are alluring to humans but which are less so to them.
How can a player incorporate this into their RP? Help them understand that their elven character has been around most likely for at least a century, and ask them what hundred year old humans are like. The parallel isn't exact, because after 50 most humans begin to think of death and the end, which elves don't, but that gentility, wisdom and peace that the fortunate elderly have are more in tune with an elf's nature than the fiery disposition of a 20 year old.
Elves should have deep passions that rarely come to the surface, an appreciation for art and music that stems not from their simply being 'artsy' but because over time, beauty is the one true constant that retains its appeal, especially simple, natural beauty. However, nobody lives that long without developing strong convictions and beliefs, deeply ingrained codes and morals that they follow, and thus elves should also be staunch advocates of certain ways of living. Whether this is a more pacifistic philosophy that stems from having witnessed the cyclical futility of violence, or an intolerance for racism, discrimination, small mindedness or cruelty, an elf is most likely to have grown into a deeply rooted belief structure that is far more powerful and greater than that which most humans can imagine.
While your player will no doubt spend most of his time caught up in the moment, and play his elf like a regular person, strive to remind them through your descriptions with hints as to their age, their outlook on life. An ancient tree to others would probably have been planted when they were young; a beautiful sunset could remind them of one they saw seventy years ago; a shopkeeper's face could remind them of an old friend long dead these past five decades. Little hints and details like these will help them stay IC, and remember that they are part of an ancient and wise race.