First, since you live in the Peoples Republic of Cambridge, you had better check with the local Conservation Commission before you do anything. They tend to take drainage projects near a wetland (swamp) very seriously.
Second, if the soil is really clay, and is saturated, the drain you are proposing will do absolutely nothing during the wet season, since the water table will not permit drainage. So before spending time and effort, you should get a level and verify that there is available drop between the water table at your backyard and the water table where you propose to drain to. If you have the pitch, you could theoretically drain into a barrel full of stone, which might work. Then again, if the soil is as bad as you say, the barrel will simply fill up, and not drain. Best to find a spot with permeable soil to drain to. But as I said, check with Conscom first, they will blow a cork if you are messing with a regulated wetland.
Second, if the soil is really clay, and is saturated, the drain you are proposing will do absolutely nothing during the wet season, since the water table will not permit drainage. So before spending time and effort, you should get a level and verify that there is available drop between the water table at your backyard and the water table where you propose to drain to. If you have the pitch, you could theoretically drain into a barrel full of stone, which might work. Then again, if the soil is as bad as you say, the barrel will simply fill up, and not drain. Best to find a spot with permeable soil to drain to. But as I said, check with Conscom first, they will blow a cork if you are messing with a regulated wetland.