Talking was the best way for me, too. Maybe not about painful things (if you have any with them) just yet, but chit chat. That's how I started. Then I'd tell them about my day. Talk about my friends, who they are (I left out the things they wouldn't like, i.e. Kimberly is the biggest ert in the world, yeah you may not want to say stuff like that xD)This was gradually. Soon I became comfortable with them and they were comfortable with me. Well, except my younger brother. I am still awkward with him, but that's because he's prejudice (claims it's a joke, but I don't think so), still going through puberty, has flashes of rage (hormones, man), and is obsessed with working out. =_= Not my cup of tea.

i used to be the odd one out in my family when i was in my teens... (im 26 now) i think i was very 'distanced' until i turned 23... i wasn't close to any of my siblings, nor my parents... we dont fight. we just dont talk too much... and you know what, i suddenly realized that i could be growing older and not be close to them... so i started making moves... just like what your doing now, i got worried...

find a hobby that members in your family like... LEARN IT. and if you ask them about it, they wont get annoyed if you ask them nicely... i forced myself to learn computer games because of my brothers and my cousins.... i dont like computer games too much, but because i wanted to bond with them, i endured it... turns out it was fun if i play it with them...

then with my dad... i stay close to him... we dont talk but i try to sit myself beside him, watching a movie he doesnt like... i just sat there feeling bored, but i noticed that after sometime, we started talking about it... and now i regularly bug him in his room to watch tv even if i have more than tons of stuff to watch inside my own space...

my mom... she was the easiest to get close to... i subtly complimented her cooking and asked her to teach me one time... now, sometime she asks me to take over cooking for the family...

my sister... she has kids... what i did was bonded with the kids first before her... i would talk to her about the cute things her kids would do.... i got closer to her husband too...

sorry for my long msg but i think what your asking help for is really important... and when you get older, you're going to start realizing that family is actually more important friends... because you outgrow your friends... but never your family... i used to rebel a lot, but now i am doing much better... best thing i did was to introduce my friends to my family... i bring my friends home, so my family will see what kind of person i am to them and my friends...

learn stuff, make them need you ;)

Talk to your family more. It's easy for me.