"It's basically all rewriting. Most of the process is rewriting rather than writing." Richard Curtis
MAKE IT DRAMATIC
A sketch is a mini play. And just like a play, it should contain drama and conflict. Nothing can be more boring than a sketch with a group of characters who just sit around and talk.
You're probably thinking, "What about Monty Python's Four Yorkshiremen sketch? All they do is sit and talk - and it's about the distant past. But it's funny!" But the four old farts are competing with each other as to who suffered the most in their youth, each rubbishing the others' pain stories: "Luxury!". So there's real conflict.
Get your characters to rub up against each other. Make sure there's something at stake between them. Give it a bit of passion. The more your characters are emotionally engaged, the funnier it will be.
SKETCH CHARACTERS
All sketch comedy is character comedy. Even the sketches which depend on warped/crazy/ecccentric ideas need characters to bring them alive. If a sketch depicts characters who are cardboard, lifeless and cliched, it's going to struggle to be funny however brilliant the concept.
You don't need enormous in-depth analysis to bring your characters to life. Sketch people are cartoons. They are very simple. Think of their basic emotion in the sketch. Is it angry? Maybe it's inappropriately calm. Or highly scared. If you can't think of their emotion, then think of their situation and what feeling they would have. Everyone has emotions!
If it helps, give them the name of their emotion: Ms Furious. Mr Embarrassed. Ms Confused. Infuse EVERY line they speak and thing they do with that emotion. Don't be afraid to exgaggerate it. Keep the emotion consistent throughout the sketch, except maybe at the end when you get to the payoff. If you portray big, simple emotions, you're more likely to enliven the sketch with conflict. Make them talk in the way people feeling that emotion talk, make them react in that way.
Is there any jargon you can give them? If they belong to a profession, how do people in that profession talk? Would a regional accent be appropriate? Don't overdo any accents, but if you can give them the odd phrase in a dialect you feel confident with, it'll help bring them to life. Are they brusque and abrupt? Make their sentences short. Do they prevaricate, are they uncertain? Make their sentences end with question marks. Are they inarticulate? Make their speech jumbled.
A sketch which contains lively, non-cliched characters is 100% more likely to be funny.
ENDING THE SKETCH
We're often advised to end a sketch with a twist, but this isn't always easy. If you get really stuck, look back at what you've written. Is there anything you can reincorporate? It could be a big part of the setup, or just something one of the characters have said in passing. Just bring it back in, if possible with a twist or a different interpretation. It could give a nice feeling of topping and tailing the sketch.
Is there anything in the set you could use? Could any of the characters be holding a prop suggested by the sketch? For example, if your sketch is set in an office, think of the wealth of equipment and things lying around with comedy possibilities. Any of these could give you the pointer you need to finish the thing off.