It is very important in the world wide web of competition that you let your customers know you do appreciate them. Communication is the key.
I cannot tell you how many times I've purchased items on the internet without a word from the seller. Even if I receive an item ok or if there are more items I'd like to purchase, I will not return to purchase from a seller who does not communicate with me. I'm sure many others are like me in this sense.
What types of communication are customers looking for? First of all, they should be thanked via an email from you within the first 24 hours. If you don't currently do so, you should check any email connected to your website at least once every 24 hours. In the thank you email, you can also tell them how to reach you if they have any questions. If they purchased an instant download, ask them at that time if they received it ok. Occasionally downloads fail.
If your customers purchased tangible items, you should email them to let them know once the item has shipped. In this email, include tracking and other pertinent information. If there is going to be a delay in shipping of more than a day, you should also pass this information along to them.
Track the package yourself. Once it shows that the package has arrived, check with your customer to be sure they actually received it. Let's face it; sometimes those packages are dropped off at the wrong locations. You should probably also check to be sure that they are satisfied with their purchase at this time as well.
Don't forget to wear your virtual smile. People can read agitation or impoliteness as easily as they can see it. Once you've completed all of these steps, you will probably have a customer for life.