First of all, your Bitcoin Core client should be fully synchronized with the network, as @PieterWuille stated. This means your client should download and validate the entire blockchain. This may take a while to do because of the current size of the blockchain that is at roughly 124 Gb (Go have a look here). This is why this process might take a long while to complete, and your wallet will only reflect your transaction after it has synchronized.

However there are other possibilities that you can use if you aren't looking into heavy bitcoin mining and usage, or for starting purposes. You can have a look at bitcoin wallets (eg. Multibit, Bitcoin Wallet, and Breadwallet just naming a few) rather than looking at bitcoin core, just for starting out. There are also some nice online wallets and mobile wallets you can use, however, all wallets have some pros and cons to them, and maybe the best thing will be is to first read up about all the different wallets available, the main bitcoin site is a nice starting place together with the bitcoin wiki.

However, there is a small catch. Because your bitcoin has already been sent to your bitcoin core receiving address and is currently in the blockchain, you will have to wait for it to completely download to receive that bitcoin, or you can maybe read up on transferring your private keys but I am not very familiar with this and thus not sure if it will work.