Don't worry so much about likeable, as complex and believable. Audiences aren't necessarily interested in the nice guys/gals, they want to be with characters who are engaging. Make your characters struggle with something, that's the most important thing. Stories are boring unless characters are struggling. Maybe your character has trust issues, but now is in a situation where she HAS to trust someone else. Maybe your character was callous in the past, and is trying to make amends. Maybe your character is sweet and bubbly, but is now forced to adopt a more cynical worldview to survive.
Give your characters a past. Has he never forgiven himself for quitting football in high school, because he realizes that he's given up on lots of things since then? Does she still feel uneasy with some of the cruel things she said to other kids in junior high?
Give them relationships, even if its information that you know you'll never use. Does she fight with her mom because they're too much alike? And perhaps, then, when her boyfriend says she plans too much, she freaks out because she always hated how her mother overpacked and overplanned all the time? Does have a hard time reconciling what he likes about his older brother with the fact that his older brother grew up to be an alcoholic? Does that make him irrationally angry when his girlfriend gets a little too drunk at a company party?
Give them goals, even if they're small ones. Has he wanted to be a doctor his whole life? Is she saving up for a weekend getaway with her best friend?
Put them in situations where they right thing to do (be it morally right, or just the smartest thing to do in a situation) conflicts with what they want to do. Maybe he knows he should tell his boss that a co-worker does coke on the job, but he struggles because his used to lie to his parents for his brother, and betraying the friend would feel like betraying family. Maybe she is a super honest person with who's been raised to believe that lying is the worst sin, but now she has to lie to protect her sister from judgmental parents - she has to fail one or the other.
Remember that audiences like little things, too. They'll notice and appreciate that she only chews grape bubblegum. That he doesn't feel quite awake in the morning until he's had some green tea (and feels awful when he travels, because he forgot to bring tea with him and the black tea at the diner won't do). That her purse is crammed full of old receipts she never cleans out (and thank goodness - because when she unexpectedly needs to provide an alibi, she can prove she paid for waffles at 10:30 PM). His wrist feels naked without his grandfather's watch.
So yeah... it's a combination of all these things. Give them a past, including how they were raised, the moments they're most and least proud of, what was the most joyful and traumatic moments, who influenced them. Give them relationships, both deep and casual. Put them in situations where they struggle, that challenge what they believe and force them to change. But don't forget the little quirks, too, the humanizing traits - which, you never know, could become important in unexpected ways.
Try interviewing your character. I do this all the time. I grab two different color pens - one that's for their voice, and one that's mine. I talk to them on paper, and they tell me surprising things. There are also all sorts of character questionnaires online that you can full out - truly detailed sets of questions.