Insert implies that you are putting something in between two other things or into something.
When you add something, you are tacking it on to something or possibly putting something into something else like a bowl.
Insert is also more technical sounding so people might use it for directions concerning electronics and mechanics. Insert also can imply sticking something into something else, such as "Insert your money here." "Insert your cd into the cd player."
For example:
You should add some more milk to your batter.
Add eggs to your shopping list.
Insert the engine here. (The engine goes here.)
Insert your money here. (Your money goes here.)
Hope this helps.