There's a well-known (in certain circles …) doodle by Bill Watterson wherein he shares his writing process, which pretty much consists of staring blankly into space, waiting for inspiration. I imagine this holds true for a lot of cartoonists – it does for me, at least. Which makes writing about Writing a bit of a challenge, as I can't give a simple set of directions and send you on your merry way. I think the most I can manage is some random observations, which I'll try to tie together as best I can.
When you're writing, you're ultimately trying to make a connection with other people. This is true whether your works are shamelessly-autobiographical or glorious celebrations of all the wondrous noises, odors and fluids that the human body is capable of producing at any given time. You're sharing some insight, small or great, about how you think, or what sort of experiences you've had or even just what you find funny, sad or merely entertaining.
At least, you should be. There's a lot of temptation as a writer, especially when you're just starting out, to cater to an audience or to try to make your mark by defying all conventions. That just leads to burnout and frustration. If you start off by creating something that expresses yourself, you're a lot more likely to see it through; people focus on the “know” in “write what you know,” when it's the “you” that matters.
Now to try to bring this back around to comics. There are a lot of people with very strong opinions on what constitutes “good” writing in comics. Some will decry the three-panel format, with its setup-beat-punchline structure. Others will say, “Avoid decompression! Keep it snappy!” And if you indulge in certain tropes, be prepared for much eye-rolling. It's up to you to determine which criticisms to take to heart and which to brush aside.
So, be brave, little cartoonist, and write what feels right, not what you hope will qualify as “good.” Be open to criticism, but trust in your gut. And let your readers enjoy your work for what it is, instead of hoping they'll accept it for what it's trying to be.