You know the rules and the basic ideas. Here is how to get stronger on this site.
Every day: the Daily Tsume
One classical problem a day, the same for everyone, with a streak. Mondays and Tuesdays are 1手詰, Wednesday to Saturday 3手詰, Sunday 5手詰. You don't need an account to play; sign up to keep your streak.
The puzzle map and themed packs
The puzzle map starts with mate-in-one and grows as you solve. Themed packs — drop mates, sacrifices, lance and knight — each end with a harder boss puzzle, and finishing one unlocks a new board or piece set. After every solve, Explore lets you try every defence and watch it still get mated.
Tsume Rush
As many mate-in-ones as you can in three minutes. It's the fastest way to make the patterns automatic.
Games
Play the computer at Beginner or Easy until you win regularly, then try casual games and the ranked queue. After every game, open its review: the engine marks your mistakes and shows the move you should have played.