I want to make Personal Weather Forecasting System.I have measurements and figured out everything except the thing that how will I be able to fetch the data to this system. I am thinking of using wifi but have no idea about how it works and how to do that.I haven't worked on this before.I want easiest possible way to do this with my android phone. I tried to find it on google but found nothing. Please suggest me some ideas about how to do this and which wifi model I should use.
You are asking how to send data over Wifi and an ESP8266 is probably the best choice for this. It can work in a couple of ways. It can be configured to present your Mega with a serial interface and it sends anything you send to the ESP over the Wifi network and it will appear as serial data on the other end. That means you are going to need to program you Android app to read this data and make sense of it. If you want to go this way you need to research ESP8266 and the AT command set. There are plenty of threads on here about it.
But if you actually want to make your life easy you want to look at using the ESP8266 as a Web server. You Mega will send data to the ESP8266 via serial. The ESP will interpret this data and prepare it for some pretty web pages, when ANY client (not just your Android phone) request a page the ESP will send it just like any other web server would. You could even upgrade the ESP web server to support REST and provide the clients with a method of controlling aspects of the weather station. If you want to do this there are plenty of examples with the IDE (after you install the ESP board manager).