First you need to head to your state's website. If you don't know it, it is simply unemployment.yourstate.gov. You obviously need to put the name of your state into the 'your state' bit of the web address.
If you have previously created an account on the website then simply sign in with the username and password you used for your other visits. If you do not have an account then you will need to sign up. You will need your social security number in order to register. You will then be asked to create a password. Think about what your password is to be and try and make it very easy to remember, yet hard to predict by others.
Once you have gained access to your account page on the website then you will be able to view the status of your claim. It is likely to say pending if it is still being processed. Otherwise it will state that it has been accepted or denied.
If you have any difficulties it is a good idea to contact your local government office. They will be able to talk you through the status of your unemployment claim and explain anything you don't quite understand.