Ideally, the protagonist should be likable and the antagonist ought to be unlikeable. But the line can be blurred and you have to choose what's best for your story.
How can you manipulate this aspect?
Think of traits you associate with people you like. They could be kind-hearted, selfless, funny, helpful... Show it through action (make a character risk their life to demonstrate they are selfless).
Or make other characters talk about them in positive ways. Their actions have made such an impact they feel compelled to tell others about them. Great deeds and heroic acts make people talk.
How can you make a character unlikeable?
It's said if you want a reader to dislike a character have them kick a dog or kill it.
Think about immoral actions and all those traits we generally dislike in others: lies, deceit, treachery, and murder.
Empathy
As readers, usually we engage with characters we relate to, that feel the same way we do, that endure the same conflicts, and face similar dilemmas. Give them challenges and make the reader see how they overcome them.
Think of someone you admire and ask yourself why. Do you share something in common with them? Do they possess a trait you wish you had or that you want to develop? Do they impress you with a skill or talent? Have they conquered a fear you hold? Now transfer those traits to your character.
The secret snapshot technique
It's a technique to really open empathy's-door for your characters. It's a way of discovering and revealing the most profound, darkest aspects of your characters, those that will marry the reader to your character and their cause. One that exposes the vulnerabilities of your character, giving them an emotional and empathetic edge sharp enough to stir the emotions of your readers.
Think of a truly private memory, a secret most guarded, something you try to forget. It has to be a memory so secretive, that if a snapshot or photo of it existed it would be locked away and hidden from the world.
When you've come up with your example, ask yourself whether this is something you'd lock in a box and bury deep in the woods. If yes, think of another. You want to reach deep into your emotional memories to find those most personal.
The bravest writing someone can do is to explore the recesses in which the secret snapshots of their friends, enemies, and themselves are stored.
It's the job of the writer to expose a character completely.
