In order to get paid from your customers when they place their orders, you will need to have at least one payment gateway set up. To setup a credit card payment gateway:
Go to your Shopify Admin > Settings > Payment Providers > Add a Provider.
If you're based out of the United States, Puerto Rico, Canada, the United Kingdom, Ireland, Australia, New Zealand, or Singapore, then you can use Shopify Payments as your payment gateway. This is the best/most-integrated option for payment gateways, so it's definitely the easiest to use, with the cheapest rates (for most merchants). The only time you would want to use a different payment gateway, if you're from one of the above countries, is if you're selling Prohibited Items (such as: sex toys, drug paraphernalia, event tickets, in-game currencies/items, etc). If you can't use Shopify Payments, then I would recommend looking into Authorize.net as your payment gateway.
In addition to using a credit card payment gateway, you can also add alternative payment gateways, such as PayPal, BitCoin, or Manual Payment methods (ie. cash, bank deposits, etc). If you decide to add PayPal, I recommend using the 'PayPal Express Checkout' as it's the easiest to setup and doesn't cost anything extra per month.
If you end up using Shopify Payments, you will only be charged a 'credit card rate' per order. This rate is determined by which Shopify plan you're on and is usually between 2.9% and 2.4% + 30c.
If you end up using a third-party payment gateway, such as Authorize.net or PayPal, Shopify will charge you a 'transaction fee' instead of a credit card rate. The transaction fee is determined by which Shopify plan you're on and is usually between 2% and 0.5%. You will need to keep in mind that the payment gateway you go with will most likely charge you a 'credit card rate' themselves. This means that you will have to pay a 'credit card rate' to your payment provider, as well as a 'transaction fee' to Shopify -- which is why it's usually cheaper to go with Shopify Payments as your provider than a third-party payment gateway.
There is an exception to the above rule though. If you use multiple payment gateways, but one of them is Shopify Payments, then you will not be charged a 'transaction fee' on each order. For example: if you have Shopify Payments enabled, and PayPal Express Checkout enabled, but a customer pays for their order via PayPal instead of Shopify Payments, then you won't be charged a 'transaction fee' from Shopify (since Shopify Payments was enabled as an option) -- you will only be charged a 'credit card rate' from PayPal. In short, as long as Shopify Payments is enabled as an option for your customers to pick from, then you will never be charged a 'transaction fee', and you will only be charged a 'credit card rate' from Shopify on payments that go through Shopify Payments as a payment gateway.
Need more help with this step? Check out Shopify's help docs for payment gateways by clicking here.