Inventory control can be as simple or as complicated as you want to make, with many different examples to be written based on the different payment providers available through eCart.
Basic inventory control could be a simple Quantity field in the database - easy enough - but then how you go about updating stock once purchased is a little trickier.
For example, if you use PayPal then you would create an IPN script (see their web site) and introduce WebAssist behaviors to the IPN page to update the stock records as the script parses the content of the cart.
Different payment providers would provide examples of their own scripts if they support this kind of thing.
You could also manage the update of the stock on a thankyou / confirm page of your site, but this isn't necessarily reliable and I prefer to use the back end processing provided by the payment provider.