1) learn to know the person who your niece/nephew is
Be interested. Ask how they are doing, what they want to do when they grow up, etc.
Be encouraging, empowering, supportive and listen
2) stay connected
Write letters, postcards, text messages, emails; call e, communicate in all available means. Just to say you are available and attainable and you have always time for e.
3) remember the birthdays and other important dates and events
4) show up
for recitals, shows, graduations etc.
5) spend quality time together
have sleepovers, ice-cream outings and auntie/uncle-niece/nephew dates when you do things that e wants to do
6) spoil e
Give them presents. Send them things. Reward them for good things, achievements etc. Give them equipment they need for their hobbies. Surprise them. Pay for classes.
7) take them to places
travel with e, take trips with e, road trips, day trips, visit zoos, aquariums, amusement parks, museums, conserts...
8) play with e
from makebelieve to board games.
Joke with them. Have an "inner joke" that's just between you two.
Teach them party tricks and magic tricks etc.
Let them do some "dangerous" stuff they are not allowed to do by parents.
Teach them some good practical jokes (that is, things that don't embarrass or hurt people) and get them novelty items like whoopee cushions and fake mustache etc.)
9) bring the sweet stuff; candy, baked goods, desserts...
10) be the mom/dad surrogate
Instead of being the boring parent, you are the cool older person that protects e and is there for e whenever e needs you.
Be the one e can count on on being on e's side.
Be the one e will run away to, and the one e confesses to. (Respect the confidentiality. Take your role as seriously as a priest. You may tell the kid that you think it would be best if e told e's parents, but you may not go and tell the parents.)
11) be a role model
Have an exciting life. Do all the things you want to do. Get the job you want. Be the kind of adult you would have wanted around you when you were a child. Become your ideals and idols.
DON'T LIE. DON'T PRETEND. DON'T TRY TO HIDE THINGS.
Make your life such that you don't need to hide anything, you don't need to wish for anything better, you don't need to be ashamed.
12) tell stories about the time when you and your siblings were small
Skip the "moral teaching" and "you should really --- more!" stuff. One of the best teachings I got from my parents was when my dad spoke about how he always tries to be extra nice to shop clerks. They are people doing their job, and it helps them give my dad better service. To the point that they actually told him if there was any specials waiting in the future or putting aside things they thought my father might like. :-D Nothing about that I should do that, but I do, and it works like magic :-D
13) be a good sibling to e's parents
Never go against the child's parents' wishes, values, goals and rules. You have to find a way to support the child without violating the trust of the parents or disrespecting them. Don't undermine them, don't say negative things about them.
Tell them what you do and have done.
The point with this is that if the child wants to get away from e's parents, they should be able to allow this to happen, because they know the kid will run to you, and they know they can trust you. The most important thing here is the child, who should have a safe environment to learn who e is.
14) teach them what you are good at
15) create an annual tradition
Take the kid to ballet, a game, an event...
16) hug them and tell them that you love them
Tell them how you admire them. Tell them what you appreciate in them. Tell them how you love them using all the Languages of Love. That is not just something you share with your lover, it's for every person you love.
17) Have a cabinet of curiosity or treasure chest, and let them rummage through it when they visit.