Select the sales order as usual and then add a payment record for it. Then mark the order payment status as paid, etc.

When I click on Add New in the payments tab there are Authorize, Manual Authorize, Purchase, Manual Purchase options. Which one do I use? Then do I have to click on save order or place order action link to apply? Thanks.

It depends on what you want but normally you would do Purchase if you have a payment gateway setup'd. Here's what they mean. These are common credit card processing terminology used in the industry.

Authorize:
Pre-authorize the amount. Money is not deposited in your account until you Capture it (the Capture button becomes available after you have Authorized it). e.g. This is normally how it works when you pump gas at a gas station. The machine first pre-authorize a large amount in your card (say $50). After you have finished pumping gas, the machine knows what is the actual amount pumped (say $45) and they capture it (note the balance of $5 is not deposited into your account). They do this to protect the gas owner in case the car drives away.

Purchase:
Charge the card and deposit money into account immediately.

The word Manual in the buttons mean you're performing that operation outside of the Storefront using the gateway's provided user-interface. e.g. Most merchant payment processor provide their own web site for you to authorize, capture, refund, purchase (charge) the credit card. In this case, you want to mark it in the Storefront using the Manual buttons to reflect what you did. It's just for history keeping, which may be important if ever the customer comes back in 2 months and disputes an item paid or not paid. You won't have to search different sites to look at what was charged or not.

You don't have to Save the Order button unless you also changed some other settings at the order level (e.g. if you changed the Payment Status = Paid).

Thanks,