If you want to see applets, please check browser requirements . If no crossover was performed, offspring is an exact copy of parents. There are many things that can be implemented differently in various problems. First question is how to create chromosomes, what type of encoding choose. Encoding, crossover and mutation are introduced in next chapter.
Next questions is how to select parents for crossover.
Also you may think, that making new population only by new offspring can cause lost of the best chromosome from the last population. This is true, so so called elitism is often used. This means, that at least one best solution is copied without changes to a new population, so the best solution found can survive to end of run. Some of the concerning questions will be discussed later. Maybe you are wandering, why genetic algorithms do work.