Hi Dana Kadi,
Well, it depends .If you ask from me, the best way of doing migration is by setting up coexistence
between both Exchange 2010& 2013 servers : http://theithollow.com/2013/04/microsoft-exchange-2010-to-exchange-2013-transition-part-1/
But using this method, expenditure for setting-up both environments could go very high &
along-with that, your data may be at risk all the time. Moreover, if your database size is large, it may take months to transfer your data from one server to another.
So for saving your time and efforts, my advice would be to use a professional solution for
this. Stellar, Code Two are some popular names for this. You can use any of these tools and perform quick & hassle free migration without suffering server downtime.