I am a vet (1967-73 USAF SSGT 43151E), and I get to use the VA because I am a veteran and poor. If you understand how to use a telephone, you can get same- or next-day care for an emergency. If you are enrolled, and you have an emergency, the VA will eat the cost of a civilian healthcare provider. You might have to wait a long time, sometimes a couple of years, but the VA will pay the provider. Develop a thick skin for the calls you receive from the civilian provider!
The VA, in order to get people who want the service in to see the correct medical service provider, has a strict queuing system. You have to call in to receive treatment.
Apply to become a VA care recipient. You will need either the original or a certified copy of your DD214. If your claim of eligibility is successful, you're in. Get an appointment. Care for veterans for non-service-connected healthcare is free, small co-pay, or market rate, depending on your income.
I have seen people who want to get service walk in without an appointment, and get turned away. You know, morons.