If you see a path on the left or right lanes that veers off, that path leads to a junction. Junctions are where you can bank your rings safely and switch runners if you wish. Try to always enter a junction even if you don't want to switch runners; every time you do, you'll gain a banking bonus which multiplies the amount of rings that you store away. Keep it up for a ton of rings.
Complete the missions
Missions are two optional objectives that you can fulfill during a run. Completing these missions will often net you a decent amount of rings and experience, so it's worth it to finish them. You have the option to skip them at the cost of red rings, but this is not worth it at all. Save your red rings and opt to finish the missions.
Keep the combo going
One of the best ways to rack up a ton of points is to keep a score combo going. Whenever you attack an enemy, narrowly dodge an obstacle, run over a boost pad or spring, or run through a hoop, your score combo will go up by one. Get a big combo and you'll be rewarded with a ton of points.
Look for the spring pads
Spring pads are little blue circles that launch you into the sky when you run over them. Sometimes they'll give you a little safe boost ahead and sometimes they'll send you into a mini area in the sky. These mini areas are very helpful as they contain no hazards and are full of rings, orbs, and hoops. Look out for spring pads and take them whenever you can - they offer a safe place for a lot of points.
Upgrade your characters
Each character has a special score modifier on them. For example, Sonic has a distance score bonus. Depending on how far you run, you'll earn bonus points. On the other hand, Amy has an enemy score, which gets you bonus points depending on how many enemies you attack. You can increase the bonus by upgrading Sonic. Upgrading characters costs a hefty amount of rings but it'll help boost your score.
Utilize the sprites
Sprites are power-ups that help you on your current run. They can either be one-use or last forever. They will boost certain aspects of your character, like give you more points for a certain action, increase the length of your dash, make certain items appear more often, and so forth. You start with only one slot, but you can buy two additional slots for red rings.
Always enter the junctions...