The mouse explainer in the upper right corner of the Ipe window tells you the function of the mouse buttons at any time. In particular, it tells you about the current object type. The variant selected for a given object type will remain in effect even when you leave this object type and come back to it later. Note that you can also specify the default variant for some object types in your configuration file.
The next chapter will deal with the different object types in detail. As a general rule, the clicking the left mouse button starts creation of an object and adds more points to it, and the middle mouse button serves to place the final feature of the object and thus to terminate the creation. Text objects deviate from this scheme. While creating a text object, the mouse buttons serve to cut and paste text. You have to press M-e or RET to end text creation mode. (This makes sense since you have your hands on the keyboard anyway.)