I've seen 18 weeks for a "hybrid" red-sex-link and up to 26 weeks for my "I don't want to grow up" Buff Orpington. In the beginning the eggs will be small, about 60% of their full grown hen size, as the winter progresses the eggs get a little larger, but next Spring they are usually full sized.
A way to tell (not in weeks or months) is to listen for the peeping to stop and the "singing" to begin. That's when they start to make the "bawk, bawk" sound softly as they wander around the coop. Within a week or two, you'll start getting eggs.
We have ten chickens, four from last years flock and six new ones from this past spring. They all follow me around the yard and come running whenever I go outside. They come to me when I whistle, or make the "bock bock bock" sounds. They've recently started responding to clapping like when we call our dog in. Our neighbors probably think we are nuts making chicken sounds in the yard, but who cares haha, they're like our pets. They let me pick them up, and will walk right up on the deck to lay down and stretch out in the sun when I'm out there. A couple of them have tried to go through the doggie door while following our Jack Russell Terrier around!
They have been a huge help weeding the flower beds but I've given up on mulching considering it doesn't last more than five minutes and then there are ten chickens making little burrows in the mulch and dirt. We plan on raising more next spring and sell the eggs in our neighborhood. Right now we just supply our families with eggs every week.
I am really new at this, but so far, my chickens have laid their first eggs within a week of doing the "egg laying dance," when they squat low, hold their wings out a little, and tap their feet really fast. They do this when you get close to them, it's really obvious and REALLY cute and funny!