With everything in one table you'll have to use something like a DLookup. assuming the field you want to display is called "CurrentProject" it would look something like:
2 cents: This actually doesn't sound like a project suited to access. At least not the way you have it set up. You might have more luck acheiving your desired output thru prublisher or even exel. Generally if you can build a database with only table, there's not really a need to do it access. Excel will work just fine.
=dlookup("[CurrentProject]","[StaffDetails]","[StaffName] = 'Andrew Davis'")
This doesn't mean you shouldn't try, but you may want to rethink how you set it up. (first name and last name should always be seperate fields). Put all of your employees and their details in one table. Put their projects in another. Now you can not only track their current project, but keep a history of all of the past projects as well. You can add other tables as you go. But it makes the whole think more dynamic and user friendly.