Here are the key steps to migrate from Exchange 2010 to Exchange 2013:
1. Prepare - Install Exchange 2010 SP3 across the organization, prepare Active Directory with Exchange schema extensions, validate Exchange 2010 Client Access connectivity
2. Deploy Exchange 2013 servers - Install new Exchange 2013 Mailbox and Client Access servers
3. Obtain and deploy certificates - Obtain and deploy SSL certificates on the Exchange 2013 Client Access servers
4. Cutover mailboxes - Use cutover or staged migration to move mailboxes from Exchange 2010 to Exchange 2013 servers
5. Redirect clients to Exchange 2013 - Update autodiscover and DNS records to redirect clients to the new Exchange 2013 Client Access servers