As mention in title you can use your android phone as a Wi-Fi router in simple steps "setup Wi-FI hotspot" , If you use 3G, 2G or any data Internet connection in android device from your provider (in SIM card), then you can share your internet service from your android device to other devices like laptop, mobile phones, tabs or any other wifi support devices.
This method is very useful when you don't have any proper internet connection in office, home or some outdoor places when you are meeting with friends or some parties, you can share internet service from your mobile to your friends mobiles as well their mobile to your mobile phone or laptop etc., I always using this facility when i am going outing.
How to configure Wi-FI hotspot? Below you can see the simple step of WiFi Hotspot configuration.
1 - Go to "settings"
2 - Select "Network Setting"
3 - Select "Tethering & Networks"
5 - Select "Setup Wi-Fi Hotspot"
Network SSID just put what you want to show your device WiFi in public, also you can make security password for the wifi spot, then save.
Now WiFi is active in your phone and internet is ready to share, top of the phone screen you can see the wifi icon.
Now you can search WiFi spot in other device and connect with the password, enjoy...
Hope this post will help you.