Gatsby’s lavish parties in The Great Gatsby are one of the most memorable aspects of the novel. The narrator and Gatsby’s neighbor, Nick, first sees them from a distance.

Besides actually seeing the “men and girls ... like moths among the whisperings and the champagne and the stars” (the beginning of chapter 3), Nick also sees the preparation for the parties and their aftermath week after week. “Every Friday five crates of oranges and lemons arrive,” and “on Mondays eight servants, including an extra gardener, toiled all day with mops and scrubbing-brushes and hammers and garden-shears, repairing the ravages of the night before.”

After hearing the gossip about the parties, and seeing the extensive work they entail on a weekly basis, readers witness one of Gatsby’s parties in chapter 3, when Nick attends a party and describes it in detail.

Buffet tables, champagne, streams of cars, crowds of people, dancing, and even a live orchestra all make the party a lavish affair. Hour after hour, the party seems to become even more elaborate. In about the middle of chapter 3, we read:

By midnight the hilarity had increased. A celebrated tenor had sung in Italian, and a notorious contralto had sung in jazz ... A pair of stage twins, who turned out to be the girls in yellow, did a baby act in costume, and champagne was served in glasses bigger than finger-bowls.

The lavish glamour of Gatsby’s parties, so fully described in chapter 3, is so remarkable that it lingers on in the imagination of the narrator, even after Gatsby’s death.

Very near the end of the novel, Nick says,

I spent my Saturday nights in New York because those gleaming, dazzling parties of his were with me so vividly that I could still hear the music and the laughter, faint and incessant, from his garden, and the cars going up and down the drive.

In chapter three, Nick, by invitation, attends his first of the grand parties thrown by Gatsby at his mansion. Here, Nick captures the intoxicating excitement and opulence of these over-the-top affairs, to which it seems the whole world has rushed to attend. He describes the sensuous aspects of his first experience of a Gatsby party in great detail. Here is one example of the lavish description:

On buffet tables, garnished with glistening hors d’oeuvre, spiced baked hams crowded against salads of harlequin designs and pastry pigs and turkeys bewitched to a dark gold. In the main hall a bar with a real brass rail was set up, and stocked with gins and liquors and with cordials so long forgotten that most of his female guests were too young to know one from another.

Nick captures the way the dizzying excitement and energy grow as the evening progresses into night. People drink freely, becoming more and more exuberant:

There was dancing now on the canvas in the garden, old men pushing young girls backward in eternal graceless circles, superior couples holding each other tortuously, fashionably and keeping in the corners—and a great number of single girls dancing individualistically or relieving the orchestra for a moment of the burden of the banjo or the traps. By midnight the hilarity had increased.

However, later in the novel, when the upper-class Daisy and Tom attend one of Gatsby's parties for the first time, the description becomes, at least in spots, more static, reflecting Daisy's disapproval of the riffraff, and foreshadowing, with the word "ghost," Gatsby's end:

Gatsby indicated a gorgeous, scarcely human orchid of a woman who sat in state under a white plum tree. Tom and Daisy stared, with that peculiarly unreal feeling that accompanies the recognition of a hitherto ghostly celebrity of the movies.

Nick registers Daisy's negative reaction to this party, so different from the open-minded eyes through which he had viewed his first Gatsby party. Daisy can only see it through the eyes of class and understand it as a place that invites the riff-raff to congregate:

She was appalled by West Egg, this unprecedented ‘place’ that Broadway had begotten upon a Long Island fishing village—appalled by its raw vigor that chafed under the old euphemisms and by the too obtrusive fate that herded its inhabitants along a short cut from nothing to nothing.

A great chapter for descriptions of the kind of parties that Gatsby throws is chapter 3. On the one hand this account presents us with the social elite of the day who frequent his parties, but on the other hand, the behaviour of these people is characterised in terms of their vulgarity. At one stage, Nick comments that the guests conduct themselves "according to the rules of behaviour associated with an amusement park." This can be viewed as another paradox or disparity in the novel relating to the gap between pretension and reality.

However, at first, until Nick actually attends one of these parties, he is attracted by the sights and sounds:

In his blue gardens men and girls came and went like moths among the whisperings and the champagne and the stars.

Note the attractive onomatopoeia in "whisperings." Nick observes what goes on like an outsider, looking in and attracted to what he sees, even though a discordant note is perhaps set at the end of the first paragraph with a description of the work that is needed to be done to repair the "ravages of the night before" on Mondays.

However, the bright lights and glitter seems to overwhelm Nick in one sense. Consider the following description:

The lights grow brighter as the earth lurches away from the sun, and now the orchestra is playing yellow cocktail music, and the opera of voices pitches a key higher. Laughter is easier minute by minute, spilled with prodigality, tipped out at a cheerful word. The groups change more swiftly, swell with new arrivals, dissolve and form in the same breath; already there are wanderers, confident girls who weave here and there among the stouter and the more stable, become for a sharp, joyous moment the centre of a group, and then, excited with triumph, glide on through the sea-change of faces and voices an colour under the constantly changing light.

It is clear that Gatbsy's parties are immense, lavish affairs, with no expense spared. They are deliberately designed to attract the social elite, and yet interestingly, Gatsby remains an observer of the action, rarely participating in the raucous "prodigality" that is described.

What is a good quote that shows what Gatsby's parties are like?

This is a good question. There are many places in the text that speak of Gatsby's parties. Chapter three is a good place to start. Right from the beginning the parties are set up. People not only come by cars, but also boats and planes. It smells of extravagance. 

There was music from my neighbor’s house through the summer nights. In his blue gardens men and girls came and went like moths among the whisperings and the champagne and the stars. At high tide in the afternoon I watched his guests diving from the tower of his raft or taking the sun on the hot sand of his beach while his two motor-boats slit the waters of the Sound, drawing aquaplanes over cataracts of foam.

Here is a description of the food at the parties, and once again we can see the decadence. Excess is the point. 

At least once a fortnight a corps of caterers came down with several hundred feet of canvas and enough colored lights to make a Christmas tree of Gatsby’s enormous garden. On buffet tables, garnished with glistening hors d’oeuvre, spiced baked hams crowded against salads of harlequin designs and pastry pigs and turkeys bewitched to a dark gold. In the main hall a bar with a real brass rail was set up, and stocked with gins and liquors and with cordials so long forgotten that most of his female guests were too young to know one from another.

Here is a description of the people:

Laughter is easier, minute by minute, spilled with prodigality, tipped out at a cheerful word. The groups change more swiftly, swell with new arrivals, dissolve and form in the same breath—already there are wanderers, confident girls who weave here and there among the stouter and more stable, become for a sharp, joyous moment the center of a group and then excited with triumph glide on through the sea- change of faces and voices and color under the constantly changing light.

The sadness of all of this is, of course, that it is completely shallow and superficial.