Consider any edit field which can accept values b/w 18-35.

Equivalence pertitioning In this method given i/p is 
divided into number of equivalence classes.

From each equivalence class one i/p value is chosed for 
testing.
Ex.Consider the above ex. edit field which accepts i/p 
value b/w 18-35.
From the given range of i/p value we can form  3 
equivalence classes.

i) Less than 18.  
ii) Between 18-35.
iii) Greater than 35.

 Take any value from three equivalence classes and test 
them. example 6, 25,100

3) Error guessing.This depends on the tester experience, 
domain knowledge, & common sense.
Ex:For the same above ex.i)23+,-34,5*,00,Blank,5o(Not 
zero,O),etc.

4) Cause-Effect GraphCause Effect Graph: A Boolean graph 
linking causes and effects

what you explained about equalent class partition is not
correct.that is all about boundry value testing.testing the
size and range values of an object.
 According to my knowledge equalent class partition is
testing the type of objects,ex: in a drop down box for
gender (Male /female).
If I am wrong please correct me.