The router has antenna's which "push" and "receive" data across your network to your computer and other network devices. Some routers have one antenna, some have 2, some have 6, etc. Some of them even have antenna's built inside the router so you can't see them.
Your computer has a wireless card with has it's own built in antenna (which you can't see), and it communicates with the router.
Together, your computer and router use their pre-existing antenna's to send data back and forth.
So- the short answer to your questions is No. Unless you live in a large house (or have multiple walls/floors which can cause the signal to have trouble making it through), you do not need to buy some sort of antenna.