To build the Accomploshrine you first need to build the first and second science machines, then gather 10 gold, a cut stone and 6 gears.
To make things easier, I would recommend creating a new world based on the classic+ mode, wich gives you some materials, food and tools right off the bat. You can set it to be always summer and always day aswell, just make sure you use the giants expansion - this makes it easier to get the gears.
Gold, stone and whatever else you need on your way to the shrine should be no real issue, except for the gears. You could get them from digging up graves (your sanity quickly takes a hit, drop rate is low and graves hard to find) or from picking tumbleweed in the deserts (low drop rate, time consuming) but I would recommend that you find yourself som clockwork chesspieces
Touch the shrine-thingy in the middle to wake the rook and kite him around to clear out the other pieces. Just be careful to evade the beams from the bishops. You should have 6 gears in a few moments, and then it's time to get cranking...