Sample Code:

Apex Class:

public with sharing class AccountController {  
    
    @AuraEnabled( cacheable = true )  
    public static List< Account > fetchAccounts( String searchKey ) {  
        
        String strKey = '%' + searchKey + '%';  
        return [
            SELECT Id, Name, Industry
            FROM Account
            WHERE Name LIKE: strKey LIMIT 10
        ];  
            
    }  
        
} 

Lightning Web Component:

HTML:

<template>        
    <lightning-card title="Search Accounts" icon-name="standard:account">    
        <div class="slds-m-around_medium">    
            <lightning-input
                type="search"
                onchange={handleKeyChange}
                class="slds-m-bottom_small"
                label="Search">
            </lightning-input>  
            <lightning-button
                variant="brand"
                onclick={searchAccounts}
                label="Search">
            </lightning-button>
            <template if:true={accounts}>     
                <lightning-datatable
                    key-field="Id"  
                    data={accounts}  
                    columns={columns}  
                    hide-checkbox-column="true"  
                    show-row-number-column="true">  
                </lightning-datatable>    
            </template>        
            <template if:true={error}>    
                {error}>                    
            </template>    
        </div>    
    </lightning-card>    
</template> 

JavaScript:

import { LightningElement, track } from 'lwc';  
import fetchAccounts from '@salesforce/apex/AccountController.fetchAccounts';  

const COLUMNS = [  
    { label: 'Id', fieldName: 'Id' },  
    { label: 'Name', fieldName: 'Name' },  
    { label: 'Industry', fieldName: 'Industry' }  
];  
    
export default class SampleLWC extends LightningElement {  
    
    accounts;  
    error;  
    searchKey;
    columns = COLUMNS;
    
    handleKeyChange( event ) {  
            
        this.searchKey = event.target.value;  
    
    }  

    searchAccounts() {        
        
        console.log( 'searchKey value is', this.searchKey );

        if ( this.searchKey ) {  
    
            fetchAccounts( { searchKey: this.searchKey } )    
            .then( result => {  
                
                console.log( 'result is', JSON.stringify( result ) );
                this.accounts = result;  
    
            } )  
            .catch( error => {  
                
                console.log( 'Error Occured', JSON.stringify( error ) );
                this.error = error;  
    
            } );  
    
        } else  {

            this.accounts = undefined;  

        }
    }
    
}  

js-meta.xml:

import { LightningElement, track } from 'lwc';  
import fetchAccounts from '@salesforce/apex/AccountController.fetchAccounts';  

const COLUMNS = [  
    { label: 'Id', fieldName: 'Id' },  
    { label: 'Name', fieldName: 'Name' },  
    { label: 'Industry', fieldName: 'Industry' }  
];  
    
export default class SampleLWC extends LightningElement {  
    
    accounts;  
    error;  
    searchKey;
    columns = COLUMNS;
    
    handleKeyChange( event ) {  
            
        this.searchKey = event.target.value;  
    
    }  

    searchAccounts() {        
        
        console.log( 'searchKey value is', this.searchKey );

        if ( this.searchKey ) {  
    
            fetchAccounts( { searchKey: this.searchKey } )    
            .then( result => {  
                
                console.log( 'result is', JSON.stringify( result ) );
                this.accounts = result;  
    
            } )  
            .catch( error => {  
                
                console.log( 'Error Occured', JSON.stringify( error ) );
                this.error = error;  
    
            } );  
    
        } else  {

            this.accounts = undefined;  

        }
    }
    
}  

Output: