-er: teacher (someone who teaches)
-able: teachable (able to be taught)
-ing: teaching (the act of teaching)
-ment: teaching (the process of teaching)
There are other options depending on the specific meaning you want to convey. For example:
* -able can be combined with other prefixes to create words like unteachable (not able to be taught)
* -er can be modified to create teacher's (belonging to a teacher)
Remember that the specific meaning of the new word depends on the suffix you choose.