It’s very easy! All you have to do is simply contact your local Department of Veterans Affairs Office. There is at least one office in every state, most likely in the state capital, but it varies from state to state.
When contacting the VA, just tell them you want to make a claim. The VA will send you a form. If your disability prevents you from making a claim, your local congressman or senator can send a letter to the VA on your behalf and they will open a claim based on that letter.