Congratulations, this is your chance to shine and make a really positive impression on your bosses. What you have here is a priceless opportunity. So what do you need to do and how?
First, get the code. He may not have checked everything in (the guy who did this to us did not) and so have someone with admin rights pull it off his computer and check it in for you.
Next triage the problem. Take the requirements and note which parts seem to have code written and which do not. This is the rough list of what isn't finished. It will grow as you do the next step. Then go through the code and evaluate it and run it and see what is currently working and what appears not to work even though there is code written. Add the not working parts to the list. Look for unit tests (I'd be surprised if you found them, the people who bail out just before a deadline because they know they are failing tend not to write them). Now at least you have a good idea of how bad it is. Also look through the requirements and see what questions you need answered. A lot of time, project failures come about as a result of poor requirments and a developer who doesn't want (for a myriad of reasons) to ask further questions.
Now you make your project plan. Start with a list of the questions you have from the requirements (write it up formally in a document) and then list the things you need to do to complete the work. Make an estimate of how much time each will take. Determine if what currently exists is salvageable (and if not, be prepared to justify why not).
Now have a meeting with the project manager (and your boss if they are two different people) and tell him or her the bad news. (It's almost always bad news when someone leaves suddenly and you have to pick up where they left off, good developers don't leave people in the lurch - they at least leave with a list of what they have done and what is left to do. The exception may be if someone left due to health issues.) In your discussion, you may get some of the answers you need and you and the PM may rework the project plan a little.
Follow up the meeting by sending the PM and other critical stakeholders (the PM will identify who), a copy of your questions that need to be answered and the project plan you worked out.
Now you have what you need to get started on the actual coding, so get to work.
In the meantime, you have probably been pulled off something else to salvage this project. Make sure your work is in shape for someone else to pick up or for you to pick up after you finish the project. That means the same types of things, a document where you say what is done and waht isn't and a check in of all source code (not necessariliy to the trunk if is isn't done, but somewhere that someone else can access it.
If you haven't been pulled off your existing work, then you need to work out with your boss how much time in the workday you will spend on each. This is one of those times when overtime may be needed and will be appreciated. The closer it is to the actual deadline, the more desperate management is, you may be able to work out overtime pay or a large bonus if the deadline is close. If this work is going to significantly delay the other work, then you need to make sure the stakeholders in that project are aware of that.
Once you succeed in salvaging the project, make sure to brag about that in your next performance review.