How to write different speech patterns?

A character's economic and educational background, as well as their jobs, drive most of my dialogue speech patterning.  But like structure, pacing and all the other "rules laden" aspects of writing, it's usually the story that makes me come up with the dialogue I do. 

However, personally I have a tendency to write grunts (cops, soldiers) as speaking in incomplete sentences:  Abrupt and to the point.  Trained professionals (doctors, scientists) speak close to perfect English.  Gangsters may swear more often, but depending on the story villains may sound more like the doctors than gangsters, so you can't generalize by their role in the script, either.  Surprise us!

I don't think that the pros (movies and TV writers) worry about it too much.  For one thing, they know that their scripts are destined to be produced, and so unless the casting director doesn't do his or her job each character will have a unique male/female low/high slow/fast delivery and will sound different.  Sometimes I think we get all too tied up with our medium (a written script, ie. 'sounds' are only in our head) and forget this.

Anyway, think about lots of very successful movies and TV shows:  Scully and Mulder 'sounded' different, but you could practically exchange their dialogue on the page and you wouldn't know which of the two it was.  They both spoke in these uber-educated soliloquies that nobody on earth actually does.  Then in Law and Order and its spin-offs, there's always a 'Sergeant' character who almost always sounds the same - blunt, sarcastic, etc.

Yes, you do want your dialogue to convey the message and not detract from the story.  You can toss in a lot of dialogue gimmicks, but in the end it comes down to the story. 

Hear the words aloud in your mind, and remember, people who know each anticipate what the other will say, but strangers, or professionals will not anticipate or interrupt as much.

I'm wondering if your question isn't about speech patterns but about distinct personalities. As in, making sure the characters don't all sound identical. Feel free to correct me if I'm wrong here or if they following info isn't what you want to know.

Speech patterns are dialects. Everyone from that same region will have the same dialect. As they should. It wouldn't make sense if someone from, say, Tennessee, talks like they're from London, England.

Distinct personality in dialogue happens naturally when the character is fully developed.

Anything else I can think of, is just practice and experience. It does get easier. So I'd suggest focusing more on character development and don't worry too much about speech patterns or dialects. It's okay to base characters on yourself, the way you would naturally talk. If nothing else, it's a really good writing exercise.

Check out more info in the Turn burn guide: https://www.scriptrevolution.com/guide/better-dialogue

Eavesdrop on people and listen for their cadences and phraseologies. Riding on buses or sitting in restaurants can be educational.

So many good suggestions above!  When it comes to writing distinct personalities, I'll add that it's not unusual for me to model a character off one of my family members, many of whom are/were quite the characters themselves.  It makes it easier to construct realistic dialogue when I think, yeah, that's what my hilariously inappropriate cousin or unconventional grandpa would say in that situation. 

Like Kenneth suggested, listening to others talk can be golden.  We were on a family pontoon ride a few weeks ago when my husband's uncle said something in an interesting way.  I've filed that for possible use in the future.  

Many times in casual conversation I've said, "Huh, I'll have to remember that one." The person I'm talking to gives to me a questioning look. I'll add, "You should always be careful what you say to a writer."

I think the keyword is "Pattern".  When I was a child I started every sentence with "Look....". That was just how I spoke.  I tend to use a lot of metaphor. That is another pattern I have developed.  Find one thing and make it unchanged. People will see it.