Begin - the beginning of an activity or event

    We are going to begin the activities soon.
    Do you know when school begins this year.

Start - is used when there are two steps or two parts in an action; it is used to state the specific time an action starts; start is also part of many phrasal verbs

    What time does the game start?
    We should start cooking now.

Start & Begin - many times can be interchangeable (either word can be used)

    Do you want to start/begin learning English?
    Do you know when school begins/start this year. 

- See more at: http://english-the-easy-way.com/Confusing_English/Start_Begin.html#sthash.TCdsGcfD.dpuf