Inventory Tracking

I currently took a position as an Asset Manager. The company I work for let go almost their entire IT department. Now I have the task of gathering correct asset information such as asset tag numbers, PC models, serial numbers, etc.. Other companies I’ve worked for have used the process of having tech support fill out a data sheet for every computer, printer, etc. they work on. Other than a full physical inventory, what is the best way to gather and keep asset information current?