Creating slang and dialect is an art, not a science, and there are two basic strategies: invent it, or steal it.
If you invent dialect, don't invent words
You can see that the slang used in Planescape isn't wholly made up--not even in real life. Sometimes slang is a reference to something (like a famous hunt), but most often it's just a matter of using existing words in unusual ways.
If you decide that fleugalsnorff is a local word for rice pudding, nobody's going to remember it at your table, especially if you make up a lot of words like that. But if rice pudding is called the jiggly, it's a lot easier to remember... and it's a lot more evocative, too. (I use the same technique for naming people, towns, nations, geographic landmarks, etc.)
Common words put to new use are easy to remember and give a good solid sense of the way a culture thinks.
Use words that people have forgotten
Quisling is an awesome word that most people have forgotten entirely. Bring it back!
Etymologists collect lists of words like that, and popular authors like Bill Bryson write entire books on the subject (not always entirely accurate, but that's irrelevant for our purposes).
But that's not how most of the greats do it:
Don't make it up: borrow and steal
If we look at the Planescape slang you mentioned, it's obvious that whoever came up with the Planescape dialect wanted to invoke a lower-class British atmosphere.
This is the most common and effective way to create dialect or slang: shamelessly rip it off. Tolkien's Dwarven script is inspired by Semitic languages, and just about everything on the planet Arrakis has Arabic or Islamic origins. For the record, this strategy is used not only for dialect and slang, but for culture, geography, history, art, and just about anything else.
First figure out what feeling you want to evoke
This requires some self-awareness, so sit down and write the things that are essential to you about the person/place. A strong caste system? No permanent home? Fetishizes the rules of hospitality?
Then find a real-world counterpart
You may have to do some research, but if you can identify a culture or period in real-life history with at least some of the elements you wrote down in the first step, you're practically done already.
You may be surprised to find that the cultural idea you thought was brand-new and original is actually very similar to something in the real world: our brains often pick up bits and pieces without us noticing, and then we put them together in new ways.
Use what you like
Commonly you won't find a single culture that fits your vision. That's great: take two and squish them together, discarding the bits that don't mesh. You may find new ideas as you read up on the cultures, things you'll want to add in.
...And don't be afraid to lean heavily on tropes for shorthand. Tropes are tools, learn to use them well.