Just what I've picked up on...
1.) Bishops > Knights, but use your knights early. They can be useful tracking pawns in the center of the board early in development
2.) Play solid openings that don't immediately open up your king.
For instance, as Black, the King's Indian is solid - develops a bishop, keeps king safe, and doesn't open up any diagonals for a quick accidental checkmate from a rogue bishop or queen.
As white, something like the Four Knights can work well.
3.) Piece protection is paramount. When in doubt, be cautious, and make sure at least one (and preferably two) other pieces are covering it.
I've won a handful of games when somebody thought they won an exchange that went 4-5 pieces, but I had something else covering the square they didn't imagine. Have gotten a few queens that way.
4.) Piece coordination / lines of sight is more powerful than a stronger piece alone.
Pushing pawns? Have a knight or bishop scout the squares around / in front of it.
Want to jump a knight to a square deep in enemy territory? See if you can have a bishop scout squares in that area first.
It's really all about intel, just like Fog of War in Advance Wars (fantastic game series, look it up if you dunno about it) ... the more you have, the less risk you take when moving your pieces.
5.) Don't be afraid to scout. Bishops / Rooks / Queen can track MANY squares at once. Don't be afraid to let them hang back and keep an eye on the action as it develops before risking them.
Basically, in summary ...
Play normal chess openings that keep pieces protected, develop knights / bishops quickly, and don't open up your king to any inadvertent diagonals for a quick checkmate.
Keep your pieces working in harmony (and don't take unnecessary risks of high-value pieces), and you should improve your ranking!
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I'm no master, but thought it might be helpful to share since I've seen multiple posts from people asking for advice (and not getting anything helpful).
Thanks!