(Originally posted here. Added examples.)
Here is the Geometry Methods info box tile.
Geometry Methods are the ways of making a shape with a tool. The 'GMs' are only available in the info box, not in the settings. You can switch geometry methods in any tool by typing G.
The first button is one click placement. The object will be created with the default X, Y, and rotation. Example: A recessed light fixture, since it's not stretchy and it doesn't matter how it's rotated.
Second is rotated placement. Two clicks. First is anchor point, second is angle. X & Y will be the defaults. Examples: Anything that you would turn to face a certain direction. A lot of things. Sinks. Light switches. Sconces. Centerline symbols.
Third is rectangle placement. Two clicks. First is anchor point. Second is the diagonally opposite point. The same method is available for polygons (slabs, fills, etc.) Not all objects will be placable this way; only stretchy* ones. By this method you can graphically set X & Y, but you can't give values. Example: Crown Tool in coffer mode.
*Interlude: Stretchiness. Objects are stretchy if they have hotspots in their 2D scripts at the 0, A, & B extents, OR "Hotspots on bounding box" is on in their "Details". Don't worry about this now. An example of a stretchy object is Bed 01 in the Furniture folder. The only way to know if an object is stretchy is to try it, or look in the script. Most rectangular objects should be stretchy.
For "stretchy" placement to work, you have to have a corner set as the insertion node in the settings. If a non-stretchy node (e.g., the center) is the insertion node, you get one-click simple placement. In the plan preview window in the object settings, the insertion node has a box around it. You can choose a different insertion node there by clicking on it.
Tip: When you Option-click (pick up settings) on an object, the node you clicked becomes the insertion node.
The fourth button is rotated rectangle. Three clicks. First is the anchor point. Second is angle AND length of first side (X). Third is length of second side (Y). Example: Crown tool coffer in a rotated space. The same method is available for polygons. If a non-stretchy node (e.g., the center) is the insertion node, you get two-click rotated placement.
The key is not to get hung up on "rotated". I use this method all the time for non-rotated polygons, because you can use R to set the length of both sides on the fly. Example: counter slabs. When placing an object such as a bathtub this way, you need to know which way the object goes; X is first, Y is second. If you do it backwards you get the drain on the long side.
If an object is "linear", only stretchable in one direction, stretchy placement still works. If using rotated placement (4th), the second click only sets the angle, and the third click sets the length. Using the fourth button with a linear object enables you to draw it very much like you would a line. Examples: Lots. Drawing title, crown tool in straight mode, steel and wood beams, cut lines. Sometimes it's hard to predict which side of the "line" an object will be drawn; if it's wrong just mirror it.
Choosing the right geometry method saves a lot of after-rotating and -stretching, and is therefore much faster.