My biggest piece of advice for this is that acceptable art isn't good enough to create a successful game.
That said, if you can create something that looks right to an honest 3rd party after hours of fiddling then you're not a hopeless case, you just need practice.
There are three things I suggest you do for practice:
- Find a local art school, if you can, and take a basic drawing class to learn basic techniques
- Practice drawing real scenery and objects to scale and in full
- Try to practice on larger paper (11"x17" or larger), and fill the page
- Find pieces from artists you like and try to replicate them
The more you practice with real scenes, the less time it will take you to create acceptable results. There's no easy way out of this, unfortunately. Furthermore, the more art styles you can absorb, the more stylistic tools you will have to apply to your game.
In terms of specific tools for 2D game art, you can't go wrong with Adobe Photoshop, or the GIMP if you're on a budget. Generally you can either scan a real-life drawing and work with that as a basis, use a graphics tablet system to draw directly into Photoshop, or a combination of the two.