I've never made a "regular" red wine so I"m no expert. But I make country wines out of just about anything except grass clippings. If I wanted to do a red wine, I would buy a kit that costs about $75. They are quite good, and have complete instructions and ingredients. They are easy to put together using the equipment you have. They usually make 6 gallons of mid quality wine.
I'd look at any online homebrew website and find one that you like and give it a try. As a rule, wine tends to be easier and less labor intensive. It is more forgiving than beer and unless oxygen or bacteria get into it, it's almost impossible to screw up.
If you want to make country wines, jackkeller.net has some great information.