1) Spend time with them. Quantity is just as important as quality. Of course when you are with them, really *be* with them too, but in order to really build a strong relationship you need to put the time in. In the case of small children this time may be spent with other adults that they are comfortable with present (ie their parents). You do NOT need exclusive time alone with them to build a relationship, in fact, the best way may be slowly and with others around. Don't wait for everyone else to leave. Also be open to spending time with the child on their terms, when it is good for them. Children have a lot less life experience than you do and are learning new things every day. They are sometimes tired, overstimulated, hungry, or just out of sorts and if you try to push your time agenda (ie when it's "good" or convenient for you), you may lose out.
2) Follow their lead. Watch the shows they like with them. Discuss afterwards. Color with them. Help them with their projects, but let them tell you how you can help. Listen. If they don't feel ready to do something but want you to do it instead - DO IT, don't pressure them to "do it themselves". Avoid correcting them but answer their questions directly if they ask (no "look it up!" needed). Read a book together. Bake. Play hide and seek or a board game. Watch them: do the monkey bars, swim, do silly tricks or make funny faces. Get excited about their new accomplishments and skills.
3) Don't take things personally. If they say no to an idea or an activity that's ok. If they are feeling shy don't push them to interact with you but keep trying and stay available so when they are ready, you are there. If they're having a hard time and say things that hurt your feelings try to remember that they are the child and you are the adult. Be honest with them but also own your own emotions and reactions. Apologize if necessary and accept their ways of apologizing.
4) Have fun! Kids are so good at playing... well, really they are great at plain old LIVING, and they have so much to share with us. It is so worthwhile to foster relationships with them and is beneficial both for you and the child, now and in the future.
How do you build relationships with children in your life? Did I miss anything you consider crucial that you would like to add? Or do you disagree with some of my "building blocks"?