The timeline. It takes about 25 hours for an egg to make its way through the hen's internal egg laying factory. The egg can only be fertilized in the first 15 minutes of that journey. This means if a mating takes place on a Sunday, Sunday's egg is not fertile. Monday's egg might be, depending in what time the mating took place versus the egg starting its journey. I would not count on it. Tuesday's egg is almost certainly fertile.
This is after a mating, not after they are introduced. A rooster does not mate with each and every hen in his flock every day. After a mating, a hen can lay fertile eggs for somewhere between 9 days and just over three weeks. Most people use two weeks for this and it usually works out OK.
There are a lot of variations on a mating, but a normal sequence is that the rooster dances. This signals his intent and interest. The hen squats. This gets her body spread out on the ground so the rooster's weight is spread out and not all going through her legs.
The rooster climbs on top and grabs the back of her head. This head grab helps him keep his balance but also is her signal to raise her tail up out of the way. The rooster very quickly touches his vent to her vent and hops off. The hen stands up, fluffs up, and shakes. This shake gets his sperm in the right place in her system.
Both the rooster and the hen need to do their part for a successful mating. Some roosters are brutes and can be pretty rough. Some hens resist so much they put themselves at risk. Some chasing is often involved. As long as the rooster and hen do their part, the hen winds up squatting ang the rooster is not so rough he injures the hen, it all works out.
Not all hens will accept all roosters. Mature hens will sometimes kick a young rooster's butt instead of submitting. Mature hens sometimes expect a rooster to find them food, dance for them, maintain order in his flock, and keep watch for predators before they grant him any favors. Some hens will squat for anything wearing spurs. A lot depends on the maturity and confidence of the rooster. If you are going to try something like this, I suggest you get a rooster at least a year old. I have seen roosters about 4 months old that mature hens would accept, but that is pretty rare.