There are many things you can do to improve your rank:
First, play Turf War. Sounds counterproductive, but it's a very nice tool to keep your skills sharp in the lower ranks, where everyone in ranked is a sitting duck. Turf War pairs you with players of all skill levels, so you won't fall into bad habits like sitting and shooting at superjump icons. Of course, you still need to do some ranked, but use Turf War as a palate cleanser.
Second, know thy enemy. When you spawn, the first thing to do is check for any weapons that you'll struggle fighting against. If you know they're there, and you know what they can do, you can more successfully form a plan of attack.
Third, know thyself. You need to know which weapons to be wary of, how to actually use your main, sub and special together, and what your role on the battlefield is.
Fourth, weight the game in your favor. In the lower ranks, everyone's likely to attack the objective directly, so use a weapon that can punish them for doing this. A roller can hide and one-shot them as they go past. Splat bombs can be thrown across the stage, and newbies can't dodge them very well.
Fifth, know when to quit. If you can't assess your situation properly, you have no chance of ranking up, and plenty of chance to rank down. I should know; I went directly from S+5 to S+0 in Rainmaker because I kept playing while tilted. If you find yourself unable to counter the enemy for a few games in a row, just put down the controller and walk away. It'll still be there when you come back later.
Finally, play all of the ranked modes, and use different weapons. Some modes might seem cheap, some weapons might feel useless, but when you stumble on a combination that's fun to play, it increases your skills, knowledge and repertoire. You might even find a strategy that carries over into your favorite mode. For example, I found that to play Inkbrush in Tower Control, I had to control an entire area around the Tower. From there, I could take the same approach to Rainmaker - control the entire area around the Rainmaker, and it makes pushing towards the pedestal much easier.