You can find a community college program that should only be a few years. Some universities/colleges offer more intensive programs. But having the knowledge and having the clients are two completely different things.
Honestly, you will not be successful with a home based graphic design business, certainly not so in the current economic situation where almost all advertising and marketing budgets have been slashed. Even with the education, you need to get the clients, and no one will be running to the door of a recent grad with no real life experience. Not to mention you are competing against huge graphic design agencies who have cumulatively tens of thousands of hours of experience, a portfolio that reaches the moon, and hundreds of clients.
If you were determined to do this yourself though, I would recommend the highest level of training you can find, university would be good. Or you could take multiple college courses. Graphic design is not a job but a field and there are many subfields including print design, web graphic design, etc, all of which have education specific to themselves. After graduation, I would recommend becoming an apprentice or working in an agency for a few years so that you gain all the actual world knowledge you need (cause university doesn’t teach that). THEN you can go freelance. Yes, it’s a lot of work, and a lot of time.
You CANNOT bypass education and simply work your ass off learning the programs. You. Will. Fail. You will eventually fuck up something you didn’t know about because you weren’t educated, and your reputation will likely be permanently ruined.
Web design is much easier to learn on your own, but even then education is appreciated.