A very useful boost is the Score Booster. It costs 200 coins and gives you a 2x score multiplier for your entire run. The Pack of Revivals is also useful.
Jumps
You can change lanes while jumping or go directly into a roll by swiping down. Jumping helps you get from wall to wall or from chariot to chariot.
Objects
Hitting objects will not end the game. Doing so will bring the dog closer. Swiping to rolling barrels, vases, and some boards will just slow you down. When there are obstacles ahead that you cannot avoid, aim for the ones that will slow you down.
Power-ups
The 5x Score multiplier is important for high scores. Always collect it when it is available, and improve it at the store at your first opportunity. Other useful power-ups are the 2x Multiplier, Coin Magnet, Invincible (basically one extra life), and Super Fly (allows you to bypass obstacles). The Super Jump is not as useful, and should only be upgraded after the others.