The easiest way you can hide your IP address when you go online is to use a proxy/VPN service.
VPN/Proxies work by redirecting all the websites you visit/internet traffic through their server's IP address. So the websites you visit will show the VPN service IP address instead of your personal computer IP address. While there are many free proxies/VPNs available on the Internet, the most stable VPNs/proxies usually require a simple monthly fee. The main reason people use proxies/VPNs is to get past firewalls/access certain websites/services which are blocked by their workplace.
While the websites you visit are unable to access your IP address, the VPN/proxies you use are able to detect your IP address and it is very hard to truly stay anonymous on the Internet. VPN companies are legally obligated to disclose your IP address/details if there is a court order/search warrant. Some popular paid VPN services include HidemyAss/ExpressVPN. If you are willing to use a free VPN service which serves ads, you may wish to consider AnchorFree Hotspot.