How do I GET SPEAKERS ON Dell monitor to work off my Macbook?

Do you have the Model 7,1 MacBook? That's the only one that carries sound through the HDMI adapter. (To see which model you have go to the Apple in the upper left corner and select About This Mac, then click on More Info. When System Profiler comes up check the Model Identifier.)

If you connect the MacBook using a Mini DisplayPort or Mini-DVI to HDMI adapter you will probably need to use external speakers or a stereo system for audio. The Mini DisplayPort or Mini-DVI to HDMI doesn't carry audio and there's no audio plugs on most monitors to work with HDMI since it's expecting audio with the HDMI.
If your monitor has a DVI plug you can use a Mini DisplayPort or Mini-DVI to DVI adapter. The monitor will have RCA audio plugs for use with the DVI.

Have you set the Mini DisplayPort/HDMI as the sound output in System Prefererences? If so then maybe you'll need to contact Dell support because you're good on the MacBook end.

What is the model number of the Dell monitor?

The ST2220L doesn't say it comes with speakers http://accessories.us.dell.com/sna/productdetail.aspx?c=ca&l=en&s=bsd&cs=cabsdt1 &sku=320-1629 it says "add the optional Dell multimedia soundbar for even more enhanced audio performance." It may not send audio through the HDMI port but through separate audio cables to the multimedia soundbar. The soundbar is the rectangle under the monitor screen in the picture. does your's have that?

If not you may want to go back and ask the salesman where the speakers that he promised are.

There also seem to be two 3.5mm jacks next to the VGA port in the monitor pictures. Could these be for audio?