how long will it take for me to see big results on arms from lifting weights?!

By two months; otherwise, re evaluate.

if you do curls, dips and pushups
prob never you might gain .3 inches if that just because your a noob

you need to do some serious ****, not that pussy ****
every 3 weeks for triceps alternate between skull crushers(you can do decline, its hard but i enjoy it more im not really a fan of it on flat) and close grip bench
and then 2 other exercise like overhead dumbell extensions for the second pulldowns with a rope or straight bar or you can do it with the D attachment and make it one arm
as for biceps
start out with barbell curls
then go to dumbell curls
then do something like preacher curls(full ROM dont try to be hercules here) or standing high pulley curls(light weight, again dont try to be hercules)


sets would be 3 for each exercise and reps 4-8
no more than 8 and no less than 4
and you can do this on seperate days but only once a week



btw
are you training anything else? if your a twig you need to work on legs, shoulders, back and boobs not just arms

18 inch arms cold

If you've just started, then about a month to six weeks. Just keep at it and don't work the same muscles each day; you need to give them time to repair after a workout.