Paypal is the most widely accepted payment gateway. Before using the paypal payment module you need to get a business account in paypal. After installing the paypal in admin, you need to enter the email address that registered to paypal. The paypla payment flow is described below

1. After selecting products to purchase, your customer chooses to pay with PayPal. Customers can also choose to use your existing checkout for credit card payments.

2. Your customer is transferred to PayPal’s secure site.

3. Your customer logs in to their account and reviews their postage and billing information. Your customer clicks Pay to make their payment, which is processed instantly.

4. Your customer reviews their payment confirmation at PayPal.

5. Your customer is automatically redirected to your site

6. Your customer arrives at the order confirmation screen on your website. You are notified of a successful payment via email

Note:
Remember to set Auto return on on Your Paypal account.
Return URL is:
http://www.your-domain.com/system/modules/checkout/checkout_process.php 

Paypal support states:

Setting Up Auto Return

To set up Auto Return:

1. Log in and click Profile.
2. Click the Website Payment Preferences link under Selling Preferences.
3. Click the On radio button to enable Auto Return.
4. Enter the Return URL. Note: You must meet the Return URL requirements in order to set up Auto Return. Learn more about Return URL.

For more information about Auto Return, please refer to the Auto Return section of the Website Payments Standard Integration Guide