Getting a High Score:
Every so often you might just get into your stride and have a really strong run in this game, and in these cases you can often get a decent score that you can rightly be proud of. However, undoubtedly the best tactic for getting great scores that are competetive among your friends is to save up your Gems for one big run. Once you have a good number saved up, wait until you are on a run that is going well - better than average at least. Then, when you die, spend your Gems to keep going. Keep doing this and spending your stockpile of Gems to get as far as possible and post as high a score as you can.
The secret to getting really high scores is to ramp up the multipliers that the developers have put in the game. Every time you complete an objective in Temple Run 2, your multiplier goes up by one. As the name suggests, a multiplier multiplies your score by whatever number it is at.