navigator.clipboard.writeText() can be used to copy text to Clipboard in Salesforce Lightning Web Component.

Sample Lightning Web Component:

HTML:

<template>
    <lightning-card>
        <div style="padding:0.5rem;background:grey">
            <div class="slds-text-color_inverse">
                Sample Clipboard Text
                <lightning-button-icon
                    icon-name={iconName}
                    size="medium"
                    alternative-text={altText}
                    onclick={handleCopy}
                    class="slds-p-around_x-small">
                </lightning-button-icon>
            </div>
        </div>
    </lightning-card>
</template>

JavaScript:

import { LightningElement } from 'lwc';

export default class SampleLightningWebComponent extends LightningElement {

    iconName = 'utility:copy';
    altText = 'Copy Text';

    handleCopy() {

        console.log(
            'Inside Handle Copy'
        );

        if (
            navigator.clipboard && 
            window.isSecureContext
        ) {

            this.iconName = 'utility:check';
            this.altText = 'Text Copied';
            return navigator.clipboard.writeText(
                'Sample Clipboard Text'
            );

        }

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>60.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__Tab</target>
    </targets>
</LightningComponentBundle>