What are the signs when the fish is about to lay eggs?

This will depend on what type of fish you purchased.

Most fish are egg bearing and unless there is a male to fertilize the eggs, then the female will either re-absorb the eggs, or release unfertilized eggs that will be eaten (such as a goldfish).
If you purchased a molly or a guppy for example, those are live bearing fish and it's not uncommon to buy a female that is already pregnant.