Failed designs are part of the process, so don’t get discouraged if it doesn’t work! Just remember why the design didn’t work for you and try not to repeat those same mistakes.
— Chevee Dodd (@cheveedodd)
Look at the games you like, and see what works, and what doesn’t work. Sharp analytical skills are a game designer’s best tool.
— D. Brad Talton Jr., Level 99 Games (@Level99Games)

Lots of good stuff in this wide-ranging interview with Richard Garfield, designer of Magic: The Gathering and other titles:

I usually encourage beginning designers to self publish, not with the eye to making an ongoing business, but to understand the market as a whole, and get a publisher to take you seriously.

Play games you aren’t naturally drawn toward, and find out why they are loved by their fans.

Play critically, but don’t lose your sense of fun.

Pay attention to the parts of a game people complain about – can the games be changed to make those people happy without taking the soul out?

http://opinionatedgamers.com/2012/07/02/the-art-of-design-interviews-to-game-designers-20-richard-garfield/

Gamers gonna game, and your game can’t break when they do.
— Jay Treat (@jtreat3)
Playtesting. LOTS of playtesting. Think you’re done? Wrong. Keep playtesting.
— Phil Kilcrease (@krinklechip)
As a game designer, it is your job to create systems that are intriguing to master without being completely baffling.
— Daniel Cook (@danctheduck)
Designing games is not easy, but promoting games is hard as hell.
— Sam Liberty (@SA_Liberty)
Games become the most fun as the players become emotionally involved.
— HoopCAT Games (@HoopCATGames)
Any game that claims to get better with repeated plays needs to be fun enough that players want to get to that point.
— UndeadViking, as quoted by Games & Grub (@GamesAndGrub)
People who wish to design games should play games. Lots of them.
— Richard Garfield, in The Kobold Guide to Board Game Design, quoted by Brett Myers (@brettspiel)
Frustration is an excellent spice, but a very poor main ingredient.
— Chris Maka (@chrismaka)