I hope you don't mind, but I've made a few notes after my corrections to try and help you understand what I wrote what I did :].

The weather is really nice today.  Beautiful blue sky and very bright sun shine! The sun is very bright, and the sky is a beautiful shade of blue!1

My feel like a summer. It feels like summer has finally arrived.2 I love summer,because lot of things.I love summer for so many reasons.3 I can't wait!!!!!

1You can use words I mentioned like "shade of" to help round out your sentence more. While this isn't necessary in casual conversation, it helps you to sound more like a native speaker :].

2 With format you had written in, "summer" would be an adjective describing your feelings. If you remove "My" and refer to summer in the general sense, you can more clearly communicate that it feels like summer.

3You can say what I wrote as a literal replacement for what you had written.  However, you would normally write a longer sentence that would have a few examples.  The format would go like this: I love summer because I get to experience the warm air, the beach, and barbequeing with friends!