her passive, it will give you some strong poke and combined with a lich bane wil cause you to deal a lot of dmg to champs but also to towers which makes you a better pusher then the main ap champs.
just get used to walk in and do an auto attack after landing a spell, it doesnt have a cd so wait for your basic attack to land after your Q to pop your E ( land Q = free E), and then auto attack again, it does insane dmg and outbursts even a veigar early game.

her Q is a lock , does some nice dmg and secures kills for your team quite easily max this spell second and it will get you kills, guaranteed.

her W is a shield which blocks some damage but not too much, helps you vs bursters with a long cooldown who can jump on you and deal insane damage but are then stuck, if you shield in time you can get a kill when they go agressive because they have no damage left after their burst.

her E is a bolb, it can be placed to view an area, to lasthit some minions or to killsteal your teammates by timing it right. this is her main ability and you should max this first for lasthitting and poking.

her R is a lazer with a great range, use it to snipe people down, this way you dont have to go agressive in lane because u can win lane just by getting kills on low hp people, gets u ahead and when the other one decides to go agressive, u have those kills and u will win the trade and maybe get a kill. max this asap, great damage !

don't go agressive after missing your Q, E will me hard to land such as your ult and then , you're ****ed.
the cooldowns on lux are long enough so that your enemy will try to abuse this, don't miss your Q !

you dont need to worry about getting outpoked because u have insane sustain with your starting items and with the E you can farm at insane range. at 7:30 spam your ability's and then fire your ult at the enemy blue if you cant see the jungler and your mid, otherwise just head back , you should have plenty of gold for your haunting guise.

for the rest its just keep poking and don't go crazy when you see the lux dmg, you need to burst them, you dont deal **** damage with basic attacks.

lux is good versus champs with short range such as veigar, if you do face an oponent with short range dont walk in for that auto attack, short range often means great damage, take veigar ult as an example, nearly a oneshot so dont mess with short ranged if you are not super far ahead. otherwise feel free to oneshot them with a Q E ult combo.
lux is countered by mobile champs (dodge skills) when this occurs try to get a lot of ganks and make sure to poke them when they got no escape (foor example when they are stuck between the tower, this is also great for shooting your ult.)
also you should abuse the blue buffs you get and you sometimes steal with your ult (look part about 7:30 spam ability's)

you should only gank when you know you will get a kill. and try to snipe people asap because your alies will get an assist for it, be ready to get praised forever because of your snipes !