Tell the reader directly. 

This is the easiest way to convey character to the reader, but also the least effective. You can say something like: "Joe was a mean, nasty person who hated children." This tells the reader exactly the information you want them to know. Alas, the readers won't necessarily believe you and even if they do, this kind of direct telling is easily forgotten. 

McGrew always tells the truth, even when he shouldn’t. He is kind. And he lends Minna money from the coffee jar he keeps beneath his mattress. (from The Facts and Fictions of Minna Pratt by Patricia MacLachlan) 

Allow the character to tell the reader. 

You can use this in a first-person narrative as a substitute this for telling the reader directly. You could also use this in a third-person narrative via quoted thoughts. " 'I'm a mean, nasty person,' thought Joe. 'And boy, do I ever hate kids.' " This really tells the reader more about what the character thinks of themself than what they're actually like. 

I felt as if the universe radiated from me, as if I were standing on the X that marked the center of the cosmos. (from Love, Stargirl by Jerry Spinelli) 

Have another character, or many other characters, tell the reader. 

You can have them muttering to themselves or talking to each other: " 'I really don't like Joe,' said Chloe. 'Yes,' replied Sam. 'He's mean and nasty.' 'And he hates kids,' added Sue." However you do it, the reader will see what the people around him/her think of the character, and that says a lot. 

She looked like a hundred other girls in school, except for two things. She wore no makeup, and her eyes were the bigest I had ever seen, like a deer’s eyes caught in headlights. (from Stargirl by Jerry Spinelli) 

Use the actions of the character. 

This is probably the most effective way of building character you can use. The reader will believe it because they've "seen" it, and it will be memorable. The old saying applies here: "Actions speak louder than words." What a person does really says more about who he is than what he says: "Joe offered the kid a popsicle, but handed him an empty box." 

McGrew always hums Sometimes he hums sentences, though most often it comes out like singing. (from The Facts and Fictions of Minna Pratt by Patricia MacLachlan )

Use body language. 

This is a variation on using the actions of the character, but it's a bit more subtle. Think about what body language can say, and use it to show your character's attitudes indirectly. Does she bite their fingernails during scary movies? Does he lean away from somebody who is trying to talk to them? What other kinds of body language can you use? 

I shook off his hand and stepped away from him. (from Journey by Patricia MacLachlan )

Use emotion. 

There are lots of ways to convey emotion, and showing what a character feels at particular times can tell the reader a great deal about what kind of person the character is. To show emotion, use physical details (like body language), revealing actions, facial expressions, quoted thoughts, dialogue or anything else you can think of that shows what they feel. 

When they finally do get around to telling me the truth of it — 'cause you can't keep a thing like that secret forever — believe me I will not forgive 'em. Not one of 'em. Not Mama, not Daddy, not Ivy June-for sure not Ivy June — so long as I live, so help me God. Even if that means I'm going to hell, which is a place I know to exist..(from The Last Payback by James VanOosting) 

Use dialogue. 

I've already said that the actions of a character can say more about them than the things they say, but don't discount dialogue entirely. The things a character says when they're not really thinking can be very revealing. To show that Joe hates kids, have him say "You're an annoying little twerp" to a kid, rather than "I hate kids." Can you see why it's more effective? 

“No!” My voice sounded harsher than I meant. “That’s Mama’s shirt!” (from Journey by Patricia MacLachlan)

Tips: 

  • Don't feel you must stick with only one of these techniques. Use them all. Combining different ways of showing the same characteristic will make that characteristic more memorable. 
  • Slip in little bits of characterization whenever you can. Try to be subtle most of the time (but not necessarily all of the time). You'll be amazed at how many opportunities you have to characterize, even in a short story. 
  • Sometimes we think an action or gesture means something, but someone else thinks it means something different. Find someone to read your work and tell you what they thought of the character — it'll help you figure out if your efforts to build character are successful. 
  • Be creative. Have fun. Experiment. Remember that, if it doesn't work, you can always change it later.