For the "ordinary" and "qualified" dividends on lines 9a & 9b respectively of Tax Form 1040, do you just enter the amounts there, or is there another form or schedule that needs to be filled out too? It looks like if you enter the numbers there, those dividends just get added in to your overall income. Is that is what's supposed to happen?
If the total amount is less than $1500, you should simply report the totals on Form 1040. If the total amount is more than $1500, the individual payers and the amount paid by each have to be listed on Schedule B and the totals transferred to Form 1040. In short, the totals always get listed on Form 1040, and Schedule B may or may not need to be filed along with your Form 1040. (Thanks to @jonsca for the correction that the threshold is $1500 these days, not the $400 stated in the initial version of my answer).
The qualified dividends participate in something called the Qualified Dividends and Capital Gains Worksheet that you fill out but don't file with your tax return. The income tax due (Line 44 of Form 1040) is computed on this worksheet, and the numbers that you write on this sheet takes into account the fact that Qualified Dividends and Long-Term Capital Gains are taxed at different rates than other forms of income.