Don't Focus TOO Much
I've noticed that if I try too hard and focus too much, I fail more often. Some of my longest runs are when I'm relaxed and just using my instincts.
Also, try not to focus directly on your character. Spread out your view to what's coming ahead so you can adequately prepare for oncoming obstacles.
Jump Before Cliff Hangers
Something that will help you survive cliff hangers (those areas where there's only one safe side to run on, and the other side is broken off) a bit easier is to get used to jumping right as you see them. As you're in the air, lean toward the side you can run on, and you'll land there.
I do this primarily because on longer runs, you're running so fast that simply leaning doesn't always get you there in time. Jumping and leaning in the air gives you ample time to land safely.
Always Complete Objectives
Completing objectives in the game increases your level, increases your multiplier, and unlocks some free coins and gems. You should always be working on the active objectives that show up on your Objectives screen.
Learn Jump & Slide Combos
One of the first things you need to master are the jump & slide combos. When you start to get a little farther on your runs, you'll notice that some of the obstacles come really close to turns. What you may not have known is that you can actually turn a corner during a jump or slide, which becomes fairly crucial. You can also cancel out of a slide into a jump as well.