I still don't fully know how to use stonemason. Almost every board I play with it I ignore it because I don't think it will be very useful. And then suddenly I lose the game because my opponent did some crazy stonemason play that I didn't even consider.
There are several basic plays for stonemason:
1. Overbuy him to get dual copies of engine components on the cheap. E.g. with a Hunting Party deck, you often want to pay 7 and nab to Hunting parties (then use the Stone Mason to clear estates). If you have $X, then you can get $2X - 4 value (excluding Stonemason). This can be viable even if the Stonemason is a dead card to you itself (either sift or trash past it)
2. Fast pile. For $12 and 3 buys you can burn all but burn an entire pile (Stonemasons), cheap components (like villages, sifters, etc.) can make 3-pile a LOT easier. You can also churn a lot of gains with playing Stonemason.
3. Point spiking. Trash Plat, gain two Provinces. A single colony buy is good for four Provinces (more than double the points) after three plays of Stonemason. With strong overdraw, you can have just $11 in cash in your engine, but in two turns gain a whopping 34 points (or overbuy a stonemason for two $5s and two $2 - like Nv/Catacombs). Province -> Gold -> Duchies is less impressive, but Stonemason with gold gaining (Explorer, Market Square, Mint, Mine, Bag of Gold, Taxman, etc.) can let an engine hammer the duchy pile quickly for the cost of two actions and some draw/sifting.
4. Down trading cards. You can set up some crazy vodoo with card gaining/Stonemason. For instance Procession/stuff can give you $5, $6, or $7 ($8 with Prince/Peddler) and even if the action is useless - Stonemason can turn it into two nice cards (e.g. Prssn -> Conspirator -> gain Sab -> draw Sab -> Stm [Sab -> 2 Conspirators]), The broad Remodel family can be really nice here.