How much time has elapsed since the first of the novel?
I assume you're asking how much time elapses from the beginning of the novel to the end. If so, you will find no definitive number; however, by examining certain details, you can make some logical inferences.
First and most obvious is the boys' clothing. When they land on the island, they have pants and shirts, socks and shoes, Piggy has a windbreaker and the choirboys even have cloaks. By the end, few of the boys are wearing much, and the clothing they do have is in tatters. Ralph is the notable exception, and he is disgusted at how irritating his clothing feels against his skin. Sun and salt and wear are all responsible for the deterioration.
Another indicator of the passing of time is the boys' appearance. Hair is longer and skin is darker for everyone but Piggy. The boys are dirty in a way that is deeper than a few days of playing outside in the dirt, and many are tying their hair back as it's gotten too long.
Also, look at the island itself for time clues. For example, the "scar" from their landing has begun to grown over. The conch shell, found on their very first morning on the island, has been worn into translucency by sun, sand, and salt.
Finally, examine the behavior of these "civilized" schoolboys. All was not perfect in the beginning, but their dramatic transformation into hunters and mirderers did not happen in a matter of mere days. It was a process which occurred over time--but not much. Most striking is the perspective of the rescuers in the last pages of the novel. We know the boys were young when they landed, but somehow we forget just how young until we are reminded by the observation of the naval officer. He saw "a semi-circle of little boys, their bodies streaked with colored clay, sharp sticks in their hands, ,,,standing on the beach making no noise at all." Obviously, their transformation probably took months, not years.
It's generally more satisfying to have a definitive answer to a question like this; however, since Golding doesn't offer a clearcut number, we can assume a specific number isn't particularly important. Instead, it is the progression of time which matters most; by examining the clues, you can follow that progression throughout the novel.