Migrating Large Database from SQL Server 2008 to 2014 I currently have on a large database (~500GB) on SQL Server 2008 that is going to be relocated to a new SQL Server 2014 server.  

My aim is to keep migration time down to a minimum.

Migrating the database by backing it up to a network share and then restoring is going to be very time-consuming.  

My plan is trying to find some way of keeping the databases in sync until the cut-over.

I’ve been looking into log shipping, but I’m not sure of the process completely (I’m not a DBA, I don’t even play one on TV), and since it doesn’t leave the database in an available state, I’m not sure that’s practical.

I’m open to suggestions, as well any tool recommendations that might assist.
I'd suggest setting up database mirroring.  

Assuming you setup mirroring in synchronous, high-safery, mode, the 2008 server will send data over to the 2014 server, as it is modified in the source database.

Once you decide to cut over to the new machine, you simply initiate a failover to the mirror database, "et voila", after a minute or two required for the 2014 machine to "upgrade" the database, it will come online and be ready to use.