"I just received my first K-1 - I'm a new investor. I know I claim the capital gain or loss on Schedule D; but where do I report the dividend received? On Schedule B or another form?"
Oh dear, you have it all wrong. The (unadjusted) capital gain is not simply transferred to schedule D (or the new form this year). You have to use the basis adjustments in the sales schedule of the K-1 and also capture ordinary income on form 4797.
Payments are not dividends. Distributions are not taxed directly however you are responsible for your share of partnership income. All the box 1-20 numbers on the K-1 have to be entered in to the appropriate forms. Turbotax makes it relatively easy, however if you have absolutely no idea what to do, I suggest getting a professional do your taxes.
Note that the IRS receives your K-1 so it is not advisable to brush this off.