Nothing can distinguishes se and ce when you hear them. However, they have completely different meanings:

    - you will always find se (or s' ) in front of a verb

e.g.: se souvenir -> to remember.

It refers to a person as me or te do, they are called "pronoms personnels réfléchis".  

Let's now conjugate se souvenir:

Je me souviens 

Tu te souviens

Il se souviens 

Nous nous souvenons

Vous vous souvenez

Ils se souviennent

    - ce will always be found in front of a noun. The feminine of ce is cette.

e.g.: ce cahier -> this notebook

       cette chaise -> this chair

Ce is used in the same place than le. However, there is a difference of degree between these two determinants: ce is more vague than le. The same difference applies to the (= le) and this (= ce).