As far as income tax (federal/IRS), if you are typical PTO, then you shouldn't have much to worry about. Some non-profits get into very elaborate situations. For instance if a non-profit starts investing in real estate and renting out the property (and it has nothing to do with it's mission), that income might be considered differently that income from a typical fundraiser.
You need to understand some basic principals and a few things about how donors can count what they give to you. For example:
1) someone who donates something to satisfy a private interest/benefit cannot claim the donation as a deduction on their taxes. (i.e. a parent "donates" school supplies to the PTO for his own child)
2) any value received must be subtracted from the donation. (i.e. pay $10 for $3 spaghetti dinner. Charitable contribution is only $7)
What you might want to do is review are some of the documents on the IRS website. I'm not suggesting you read these cover to cover.
Unrelated Business Income
www.irs.gov/charities/article/0,,id=96104,00.html
Publication 598 Tax on Unrelated Business Income
www.irs.gov/pub/irs-pdf/p598.pdf
Publication 525 Charitable Contributions
www.irs.gov/pub/irs-pdf/p526.pdf
Charitable Contributions (Substantiation and Disclosure)- This is a very nice brochure.
www.irs.gov/pub/irs-pdf/p1771.pdf
(intended for the individual taxpayer)
Frequently Asked Questions about Exempt Orgs
www.irs.gov/charities/content/0,,id=96986,00.html
This is a nice site, very clear - easy to see what you might want to read.