I want to make a Weather web part form any api. I have searched on Google but could not find any good solution. So, any link or suggestion or steps for that?
Do you know how to build a basic web part? If not I suggest you learn this first. Here's a sample tutorial: http://msdn.microsoft.com/en-GB/library/ms415817(v=office.14).aspx
Next you want to learn how to develop against web services. Helpfully, Yahoo have a tutorial on how to deal with responses to web services as XML within C# applications: http://developer.yahoo.com/dotnet/howto-xml_cs.html. Yahoo have also documented their weather API: http://developer.yahoo.com/weather/
Hopefully with these two fundamentals you know enough .NET development already to fill in the gaps.