Some general tips to "git gud":
Learn the tracks.
If you're not familiar with the tracks, play single player Cups until you are. Taking a wrong turn or not being prepared for what's up ahead will seriously hinder your chances. Additionally, many tracks have shortcuts.
Dirft, drift, drift!
You should really be drifting around every single corner, or at least attempting to. Not getting boosts from mini/super/ultra Turbos via drifting is putting yourself at a serious disadvantage against other players.
Do tricks on every jump
Tricks give you a boost when you land. Same principle applies here as with drifting.
Coins increase your top speed.
10 coins give you your maximum top speed, and every coin pickup gives you a small boost.
Experiment with Karts/ATVs/Bikes and Characters
Different vehicles, parts, and character weights give varying results. Don't just rigidly stick to one character and the same kart.
Not all bikes are the same
Some bikes have inside-drifting. That means when you drift, you lean into the curve which can help you shave off valuable seconds. Some people find them fiddly to control though.
Protect yourself.
In first place, your priority should be protection. Hang a banana peel or shell behind you to block incoming shells.