• An object to move
  
• Optional: A table of destination positions (e.g. list of snap points)

The tabletop simulator currently defines 3 different functions to move an object:

All 3 functions take vector (in the form {x=?,y=?,z=?}) to describe the destination position. Whilst both setPosition and translate will serve as an instantaneous teleport, the setPositionSmooth will actually move the object in the world. It therefore requires additional instructions. The most important variable is the collide bool which will decide if the object is able to clip through other objects on its path (which would equal false). The variable fast can normally be set to false, as it only decides if the object is moved in a slower or faster pace.

In most cases it is advisable to use the setPositionSmooth function to move an object, because it simulates object movement in the most natural way.
To actually move the object, you have to call the respective method on the object reference

To help you understand the concept, here a quote from the knowledge base:
X is right/left, Y is up/down, Z is forward/back.

Object movement requires requires a vector which describes a point in the game space. Two different types of vectors are possible: the global and the local position. Whilst the global position describes a point in the game room, the local position describes a point in relation to the center of a specific object. To obtain the current position of an object and convert it, following functions can be used:
The getPosition() function returns a vector of the form {x=?,y=?,z=?} which describes its position relative to the world.
The other two functions are self-descriptive functions which can be used to convert vectors between world and local coordinates.

The functions offered to rotate an object are comparbale to the ones used to move objects:
The setRotation function will instantaneously rotate an object, whilst the setRotationSmooth function will actually rotate the object in the world. Both functions take up an vector of the form {x=?,y=?,z=?}, where each assigned value specifies the rotation around this axis in ° (values can range from -180 to 180). The variables fast and collide do the same they did in the setPositionSmooth function.

As for the movement, it is advisable to use the setRotationSmooth function to rotate an object, because it simulates object movement in the most natural way.
To actually rotate the object, you have to call the respective method on the object reference

To help you understand the concept, here a quote from the knowledge base:
X is pitch (nodding your head), Y is yaw (shaking you head), Z is roll (tilting your head).

Now that we know how to obtain the position of objects and move them, we are theoretically able to move objects at our discretion. But how do we get positions to move our objects to without laborious chore of checking every position we need with scripted objects or trial and error?
The simple answer is: Snap points

Snap points provide a convinient way to obtain global coordinates. At first we have to obtain the respective snap points associated with an object:

This function will provide us a table with following content:

The position and rotation tables for each snap point describe its current global position as well as its rotation. The bool rotation_snap is an indicator if the snap point is a "rotation" snap point.

Using this list, we are able to move our object to a respective snap point. But there is one last thing to consider: The volume of the object. Snap points can be found on the surface of an object and are thus far nearer than e.g. a game tile would be. So the position of the snap point has to be adjusted to accomodate for the colume of the respective object. Without that, the moved object would most likely land inside the destination point, rather than on the destination point. A graphical example would be a tile in a board game that would drive inside the board instead of setting itself on the board.
For this kind of adjustment, you can write a simple function:

In this function, tile represents the respective object, move is the position vector of the snap point, which can be addressed via the following call on the table of snap points:

In my example, the y coordinate of the position will be adjusted to place a game piece on top of a board. The position has after the transaltion to be corrected again to the original value by subtracting the height of the object.
You can access the boundaries of an object, which are necessary for such adjustments, via the following call:

This will provide you with an vector of the following form, describing the maximal extension of each axis: