With the 2006/2007 release of the 'Panama' platform, it operates pretty much like Google Adwords… ads have a headline, two lines of body copy, and a URL.
You bid on keywords on a CPC basis, and Yahoo decides based on both a quality score and your bid where to show your ads.
Yahoo's platform is generally considered somewhat simpler than Google's Adwords, both in terms of sophistication of what you can do and the sophistication of its display algorithms.
Standard Match matches only an exact phrase that somebody types in; but unlike Google's exact match, it also matches plurals and common misspellings.
Advanced Match is somewhat like Google's old broad match; your keyword matches regardless of word order (as well as for all the stuff like plurals).
In my limited testing, it seems that many standard match keywords are bid really high (like 3X of what they go for on Google, in some cases). If this is the case with your campaign, I'd advise running YSM with Advanced Match, and a good set of negative keywords.
Using Google Analytics with YSM
If you use Google Analytics with Yahoo Search Marketing, you can track your campaigns just like you can with Adwords campaigns. For information on how, see this PPC Hero article.