Using LWC how to generate pdf and download it

In LWC, there isn’t a built-in way to generate PDFs, so you usually go with (Apex + Visualforce ) 

The Apex method returns the PDF as a Base64 string, which you can download from your LWC. 

public with sharing class PdfController {
    @AuraEnabled
    public static String generatePdf(Id recordId){
        PageReference pg = Page.MyPdfPage;
        pg.getParameters().put('id', recordId);
        Blob b = Test.isRunningTest() ? Blob.valueOf('test') : pg.getContentAsPDF();
        return EncodingUtil.base64Encode(b);
    }
}

import generatePdf from '@salesforce/apex/PdfController.generatePdf';
async downloadPdf() {
    const base64 = await generatePdf({ recordId: this.recordId });
    const link = document.createElement('a');
    link.href = 'data:application/pdf;base64,' + base64;
    link.download = 'MyFile.pdf';
    link.click();
}

This works well when you want Salesforce data, merge fields, and proper formatting using VF.