The link cybersage offers above will help you with free accounting-based software alternatives to common programs like Quicken, Peachtree and Quickbooks. However, to learn actual "nuts and bolts" taxes, you'll need to look elsewhere.
Believe it or not, the IRS itself offers a lot of good information related to income taxes. Publication 17 is a great place to start reading. Here is the link to it:
http://www.irs.gov/pub/irs-pdf/p17.pdf
Note the table of contents - it lays out the major areas of income taxation:
1. Determining the type of return to use when filing and filing status
2. Determining what is considered "income" that should be reported on a return
3. Calculating gains and losses on the sale of assets (and in other instances)
4. Adjusting income after totaling up your gross amounts
5. Deductions you can use to reduce your gross income amount
6. Adding in any applicable credits and calculating final numbers
I'd start there and use that as a basis for learning more 'in depth' stuff.
Most people are afraid of taxes. It's not too complicated if you break things down like I did above. Business-related taxes (especially partnerships) can be a bit crazy, but don't worry about that for now. If you get the concepts related to income taxation you can learn the other business type stuff down the road.
Look around other IRS publications after you have gone through Publication 17 - there will be expansive treatises on each of the general topics covered in Publication 17 that will allow you to go into things with more depth.
Good luck!
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