Here's a typical goofyballer vs mech game:
http://drop.sc/381497
The start isn't too typical, I proxy hatch him in response to high ground CC first and delay his base for a long time while my macro suffers terribly, but eventually attack his 3rd with a huge roach force at 200-130 supply. I get overzealous with my roaches basically figuring "I have 3 bases and a good economy, I'll kill as many tanks as possible and switch into swarm host" but this trade goes terribly, it takes me a long time to get swarm hosts out, and the stalemate begins.
I know I make a lot of mistakes from that point, but even then I think there are a lot of things I did (abducting, building spores everywhere) that were better than what I usually wind up doing in these kinds of games, but I still was pretty much at a loss for what I should have done strategically to try to win the game. Even when I kill off his army at my 4th and have a temporary advantage, his position is so entrenched with tanks/planetaries/turrets that I don't even know how I would take advantage before he just rebuilds with more ravens and battlecruisers.