Your first step is to dig through all of the documentation you have to find any and all software purchases. This included going through the previous guy's email (hopefully it's still available) and digging out the license cards from those boxes stashed in the corner. If you are lucky, someone in accounting can start pulling invoices from you. Also, go to the resellers your company has been using to see if they can pull a purchase history or license report (CDW is great for this). Don't forget to try sites like Microsoft's eOpen (eopen.microsoft.com) or Adobe's license site (licensing.adobe.com).
The next step is to audit your workstations and servers to see exactly what commercial software they are running. Try to match that up with what documentation you found to start with. My rule of thumb is that if I don't have a PO/invoice, license key or box, then I don't own the software. Then go and get quotes from your favorite reseller to see what the costs are to "true-up".
Take all of this to your manager (or the owner) and show them the situation. Be sure to explain the consequences of not licensing the software you are using, and leave the decision up to him whether to true-up, stop using the software, or use it unlicensed. I would personally document this meeting just to cover your own ass, especially if the last option is chosen.
In order to prevent this situation in the future, make sure all software purchases come through your department. Then keep all license documentation in a single physical or electronic location. Be prepared to dig your heels in when someone tries to bypass IT to install illegal/unlicense software.