I guess the best way to do it is pelt them with characters. There are lists on the internet you can use as beginning-to-get-to-know-your-characters tools, and then take it from there. Back when I was much more energetic, I used to use that way :P Even the most useless questions - "What is his favourite food?" - are useful, not because you're going to write "Benedict ate a mildly burnt vege-burger with homemade salsa and barbequed soul of the damned" or anything but because it helps get into their minds.
I like to draw my characters for the same reason, even though I'm a terrible character artist. When drawing a character you go "Well, he's stooped and hunched, and it's not a physical condition, he does it because he's insecure about his height and it's because... and...and..." or "She does -that- with her face when perplexed, but it's a new occurrence, because...." and “She wears her hair back like that because she’s not fussed about her appearance and doesn’t have any time anyway” and so forth…
Things like that make it somewhat easier to try to make 3d characters, maybe. I can’t say how to make more likeable characters – I like my flawed lunatics and my nasty sick puppy baddies, so I fail a bit at –likeable- protagonists rather than flawed antiheroes. I think setting them out to be likeable is shooting yourself in the foot. Set them out to be human, and to grow, and perhaps what they learn in your narrative, what they do, what they achieve and what or who they become will endear them to the reader. Setting out for ‘likeable’ always run the risk of simpering sweethearts who aren’t interesting unless they crack, and even then serious sue territory – characters who are rounded and human can endear the reader with their quirks, flaws and fears – they aren’t created to be likeable, they become likeable, they were created to be human so even if they cross the moral event horizon, twice they’re engaging. They might not be community police officer candidates, they might be flawed and troubled and neurotic and slightly bitchy, they might not even be people that realistically you’d want to associate with, they might smoke like a chimney with a lust for lung cancer and laugh when old people fall over, but somehow they’re so rounded, so human, they matter. Yes, I’m promoting antiheroes again, but the problem is, a lot of people try to create lovely, likeable, spun-sugar heroes and they’re so unbelievably nice they’re frankly unreal, so perfect one scoffs and so flat and un-edgy and unrealistic that even their most dramatic last stand against the antagonists elicits a yawn. Oh come on, stuff like that gets published a lot. I’ve thrown a lot of it across a room in disgust. They’re ‘likeable’ alright, but unrelatable and dull as dishwater.
What I mean is, do you mean likeable or do you mean engaging?
Anyway, I suggest doodles and odd phrases on paper and facial expressions doodled out, and a battering ram of questions. I also like to keep a file of nicely worded personality fragments and sentence scraps my mind spits out, beginnings of stories, thoughts, fears, dreams of characters who don’t exist yet, and every now and then I take a flick through. It encourages horrible franken-characters and patchworking, but sometimes it just clicks.