I am new and I did not get bitcoins
Yes, wait for it to finish synchronizing. You will not see your coins until it finishes.

(Note that the time shown is not the estimated time until completion; it represents the age of the old transactions currently being downloaded. Depending on the speed of your computer and internet connection, you can expect it to finish in a few hours to a few days.)

In the meantime, you can enter your address in a "block explorer" site like http://blockchain.info to check whether the seller made the transaction as agreed. (This is safe; your address alone cannot be used to steal your coins.)

If you don't want to download the entire block chain, you can use a different client such as Multibit, but you will have to import your wallet.dat from Bitcoin Core into your new client software. Its documentation should explain how to do that.