Engines are great in lots of circumstances, as is well know, but how do you go about building them? Is it just a coincidence that the top players end up doing better in engine games than other players? (Hint: No, it isn't). A lot depends specifically on the exact configuration of cards available, but there are some things which are generally true that will hopefully be helpful.
Build Your Draw Up First
The first mistake that a lot of players make is to get too much payload too fast, without building their draw sufficiently. This is an easy trap to fall into - it looks good, since it helps your deck have better turns economically in the (extreme) short term. You get to buy more/better stuff right away. The problem is, it ends up actually being slower in the end. The reason goes back to how engine economies can explode once you get to drawing your deck. Once you get to that point, you can pick up all those 'missed' economic pluses over the course of only a couple turns. At the end of all that, it doesn't matter that more of your turns did 'worse things', because your final product is either 'there' faster, or with extra draw stability to boot, and at that point, it doesn't matter how you got there - the resulting deck is just better.
The Development Phase
At the beginning of the game, you're pretty far from drawing your deck - you have ten quite bad cards, you're only drawing five, and you need to add more cards in order to do anything. The top priority is almost always to thin down by getting rid of your (bad) starting cards. It's the quickest way to get you to drawing your deck, and it gives you good consistency. If you can't thin, it's usually a good idea to get some sifting cards - they will cycle you back to your key buys faster.
Beyond thinning, you'll want to get the minimum possible economy in order to get the components you need. How much this is depends on a lot of things - principally what you're looking to get and what your other things currently are - but a good rule of thumb is that you need very very little to hit $4 consistently, 1-2 silvers to hit $5 consistently, and 2-3 silvers to hit $6 consistently. Be on the lower end of this when you can - extra economy is typically extra dead cards which you'll have to fight through. If nothing else, every silver slows down the rate at which you see your trasher (or whatever other good card) one slot every other shuffle. This sounds like very little, but it adds up pretty quickly, especially in your deck that wants to shuffle every single turn, and especially with that effect compounding itself.
In terms of what order to buy components in, during this stage you want 0-1 more terminals than your villages can support - in other words, terminals before villages. The reasoning here is pretty simple: there's a good chance the terminals aren't colliding yet anyway, and their effects are more important than the villages'. There are lots of exceptions to this rule though - usually when your village has some significant effect such that it's a good bit better than a straight cantrip.
The Economy Phase
One you get to the point that you can draw your deck - even if you can't do it reliably yet - things start to change. You really can't ignore building the draw aspect of your engine, as you will be adding more payload cards and/or green cards that you need to draw, and you also need to increase your reliability. At the same time, you do need to start looking to getting your economy going.
At this phase, you're looking to add a mix of cards such that you're increasing your payload whilst simultaneously reinforcing your draw and adding reliability. It's at this stage that cards like Scheme really start hitting their potency in terms of reliability (I should note that there are other applications for the card).
Specifically in this situation, the script flips from the first phase, and you want villages before Smithies. Obviously, you want to keep enough draw to be able to scoop everything up. But when it comes to over-building, you're much better served in getting extra villages compared to superfluous draw. This is because the biggest chance for you dudding out is from finding insufficient villages to get going - it's worth noting that extra villages don't hurt your chances of finding a Smithy on time, but extra Smithies do hurt your chances of making it to that Village. Of course, this isn't true when your villages don't draw you cards.
Exceptions are so many and varied that I am definitely not going to go over all of them. But I will mention the two biggest ones here: in mirrors, when you are pinched for some particular resource, you want to put a bit of an extra priority on that resource, because winning the split can be a big deal. But the biggest exception of all comes with game-end considerations, where you need to maneuver pile depletion in your favour.