Newbie help.

[Simon8x]

Am I correct in thinking that once this sync is complete my total will show as 3.00 and then is this the bitcoins are stored on my desktop?

Yes.

Bitcoin Core wallet can take days to sync depending upon your connection spped. The sync data (blockchain) is sized in GBs.
You could have used a lite wallet like MultiBit which syncs in matter of seconds.

The bitcoin is not really stored on your desktop. It is the private key in your wallet file that allows you to spend the bitcoin.

[dothebeats]

At the footer of this it also says synchronizing with network and has been like this all day (slowly moving)  Am I correct in thinking that once this sync is complete my total will show as 3.00 and then is this the bitcoins are stored on my desktop?

Yup. It will show up in your wallet once the synchronization is finished. As for the sync speed, it depends on how fast your connection is and how many peers are you connected to. The bitcoin core wallet's blockchain data is sized in GB, so don't expect a speed download of data if you have a slow connection. You might have just tried a small wallet like MultiBit or something if you don't want to have a copy of the whole blockchain.

[HeroCat]

Try Multibit - it is a much faster that Bitcoin Core  Or you can try to use online wallets too