LWCProgressIndicator.html

<template>
    <div class="slds-theme_default">
        <div class="slds-p-around_medium">
            <lightning-progress-indicator type="path" current-step={selectedStep}>
                <lightning-progress-step label="Step1" onstepfocus={selectStep1} value="Step1">
                </lightning-progress-step>
                <lightning-progress-step label="Step2" onstepfocus={selectStep2} value="Step2">
                </lightning-progress-step>
                <lightning-progress-step label="Step3" onstepfocus={selectStep3} value="Step3">
                </lightning-progress-step>
                <lightning-progress-step label="Step4" onstepfocus={selectStep4} value="Step4">
                </lightning-progress-step>
            </lightning-progress-indicator>
            
            <div class="slds-m-vertical_medium">
                <lightning-button label="Back" class="slds-m-left_x-small" onclick={handlePrev}></lightning-button>
                <template if:false={isSelectStep4}>
                    <lightning-button variant="brand" class="slds-m-left_x-small" label="Next" onclick={handleNext}></lightning-button>
                </template>
                <template if:true={isSelectStep4}>
                    <lightning-button variant="brand" class="slds-m-left_x-small" label="Finish" onclick={handleFinish}></lightning-button>
                </template>
            </div>
        </div>
    </div>
</template>

LWCProgressIndicator.js

import { LightningElement, track } from 'lwc';

export default class LWCProgressIndicator extends LightningElement {
    @track selectedStep = 'Step1';

    handleNext() {
        var getselectedStep = this.selectedStep;
        if(getselectedStep === 'Step1'){
            this.selectedStep = 'Step2';
        }
        else if(getselectedStep === 'Step2'){
            this.selectedStep = 'Step3';
        }
        else if(getselectedStep === 'Step3'){
            this.selectedStep = 'Step4';
        }
    }

    handlePrev() {
        var getselectedStep = this.selectedStep;
        if(getselectedStep === 'Step2'){
            this.selectedStep = 'Step1';
        }
        else if(getselectedStep === 'Step3'){
            this.selectedStep = 'Step2';
        }
        else if(getselectedStep === 'Step4'){
            this.selectedStep = 'Step3';
        }
    }
     
    handleFinish() {
        alert('Finished...');
        this.selectedStep = 'Step1';
    }
     
    selectStep1() {
        this.selectedStep = 'Step1';
    }

    selectStep2() {
        this.selectedStep = 'Step2';
    }

    selectStep3() {
        this.selectedStep = 'Step3';
    }

    selectStep4() {
        this.selectedStep = 'Step4';
    }

    get isSelectStep4() {
        return this.selectedStep === "Step4";
    }
}

LWCProgressIndicator.js-meta.xml

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata" fqn="LWCProgressIndicator">
    <apiVersion>46.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__AppPage</target>
        <target>lightning__RecordPage</target>
        <target>lightning__HomePage</target>
    </targets>
</LightningComponentBundle>

Output: