

Ratios . As that great sage Ralph Wiggum says, "I'm learnding!" . In the interest of promoting knowledge and accelerating the learning curve among those who haven't yet discovered the following ratios, I present to you a few tips and tricks that I've found useful in my own building.
Everyone knows that a standard Lego brick is three standard Lego plates high. This is quickly discovered in our earliest days of basic studsup building.
But there comes a time when you need to graduate to more advanced SNOT (Studs Not On Top) techniques to achieve a certain look or texture impossible with simple studsup brick and plate stacking.
When you integrate an element with the studs facing at right angles to adjacent or surrounding construction, you need to know the ratio between plate height and stud width. This ratio, which I utilize over and over again in my building, boils down to: five plates height equals two studs width.
This is important enough to bear repeating: 5 plates high = 2 studs wide. Note that the studs themselves are not counted in the height of a plate  thus, more accurately but longer to write, four plates and one tile equals two studs. For purposes of this tutorial, when I refer to plate heights, I am not counting the topmost studs. When utilizing this technique, you will need to swap out the top plate for a tile, or somehow account for the studs (see below).
Here we see that two bricks height (6 plates) minus the bottom tile (1 plate) gives us a quick and easy 5 plates high / 2 studs wide gap to slip our SNOTed plate stack into.
Knowing this ratio (and as long as you can count by twos and fives), you can now completely fill any space whose length and width can be measured in an even number of studs. 4 studs = 10 plates. 6 studs = 15 plates. And so on.
The magic doesn't stop there. A floor made of these SNOTed plate stacks will, without effort, match up right at the 3 plate level when laid directly on a bed of studs beneath. This works because if 2 studs = 5 plates, then 1 stud = 2.5 plates... and the height of a stud itself = half a plate.
Because everything works out so nicely, you can then easily build out onto this floor and lock it into place if you haven't already  otherwise nothing holds it in but gravity (or friction if it's vertically oriented in a wall), and if you tilt the base far enough, it will fall out.
To lock it in place without this, you'll need technic bricks (or headlight bricks, see below). The studs on a standard plate will fit into either two 1x1 technic bricks or the 1x2 with two holes. Or the one stud on a jumper plate will fit into a regular technic brick with the hole in the middle. To fasten the underside plate, use the technic brick / half pin combo or some kind of brick with studs on the side.
This fastening can also be done with brackets and headlight bricks, which have ratios of their own which must be taken into account.
Brackets and headlight bricks make use of halfplate offsets. Let's talk about the headlight brick (hereafter referred to as an HB) first.
What is a stud's width measured in plate height? If you said 2.5, good, you've been paying attention. The HB recess is half a plate deep, making the top of a HB, measured front to back, 2 plates wide. The little lip at the bottom created by the recess is also half a plate high.
Here we see that the extra half plate afforded by the recess on the HB allows us to bridge a 1 stud gap.
Or, since we're now aligned perfectly on a stud edge, begin counting off further 5 plate/2 stud increments. Through use of the mighty HB, we have broken the surly bonds of evennumbered stud width SNOT surfaces.
With their inherent height of 3 plates and top width of 2 plates, four HBs fastened perpendicularly will make our magical 5 plate/2 stud square.
The studs and holes line up neatly to plug into other such squares, making all sorts of interesting patterns possible.
Of course, when using this technique in a floor or wall, the outside studs must be taken into account.
Whereas the SNOTed element of the HB is recessed half a plate, the overhang on the bracket sticks out half a plate.
Add two plates and the overhang equals one stud wide.
In case you're a bit slow on the uptake, here is a bracket alongside two HBs with a plate to make up the difference in offsets.
A baseplate is the same height as the overhanging SNOTed part of a bracket, half a standard plate. Since the height of a stud itself is half a plate, we can lay a baseplate on a bed of studs, and the level of the baseplate will be one standard plate high.
This is by no means meant to be a comprehensive list, just a few of the basic tricks to get you started. Hope you found it helpful.
Addendum/mea culpa:
As for plugging studs into Technic brick holes, it evidently is "illegal," as illustrated here by Ryan Wood. Close enough to fudge it in most cases, but not exact.
