I've posted a pretty informal dictionary to help in deducing the meaning of scientific plant names. I got a good deal of this from some random book on taxonomy at the Pasadena Public Library. Since then I've added to it considerably. At first I naively picked up a couple elementary Latin books, thinking that would somehow help. I quickly learned that scientific plant names often have very little to do with Latin at all. True, the roots are predominantly Latin or Greek in origin, and the endings are nominally grammatically Latin, but the exceptions seem as common as the rules.
The rules aren't very complex. Each plant (or animal or any other life form) is assigned a unique pair of names: a genus and a species. The genus (plural: genera) is a noun, always starting in uppercase. The species (plural: species) is an adjective, always in lowercase. Lots of plants share the generic name, but no other plant shares both the same generic and specific names. Furthermore, the endings on the generic and specific names are supposed to match in Latin gender. (Latin has three: masculine -us, feminine -a, and neuter -um.) Of course, you don't have to look very long to find countless seeming exceptions, such as Daucus carota (Queen Anne's Lace) and Achillea millefolium (Yarrow). Don't ask me.
The most common non-Latin non-Greek roots are derived from people's names. For the specific name one is supposed to add -ii (don't ask me how to pronounce this). If the name ends in -er or a vowel (including y) then just use -i. For the generic name, botanists usually add -ia, like Claytonia (a lily genus), or Clarkia (beautiful evening primroses first discovered by Lewis and Clark). However, you will soon find clever variations, such as cookianum (for Captain Cook) or greyana (presumably for some dude named "Grey" who understandably just didn't like the sound of greyi).
One other general rule you'll see a lot is turning place names into specific names by adding -ensis: for example Citrus sinensis (the orange, originating in China), and Agave utahensis (a century plant found in Utah).
Pronunciation is apparently a matter of diverse preference. Very few people use classical Latin pronunciation. But that's probably because classical Latin sounds really stupid: for example the famous vini vidi vici loses some of its edge for English-speakers when it's pronounced "weenie weedy weekie". (Did I read the rules in my elementary Latin book correctly?) So to hell with it, pronounce it however it sounds best to you. The only vaguely important thing is to get the penultimate or ante-penultimate stress right, vowels and diphthongs be damned. For example Lomatium is "low MAT ee um" and Achillea is "uh KILL ee uh", while Pyrola is "pie ROLL uh" and Podocarpus is "poe doe CARP us". And in case you think a simple rule is to stress only syllables starting with consonants, Eriogonum is "airy AH go num" and Gentiana is "gen chee AH na". See this for a more scholarly discussion of Latin stress. A few things are certain: it's always the second-or third-to-last syllable, it's usually the one that sounds right to an English-speaker's ear, and there are bound to be exceptions.
The family name also has rules. Botanists have become anal about making all families end in the unpronounceable -aceae. (Most botanists I've talked to in America say "AY see ay", for whatever that's worth.) This Latin ending means "the XXX-like ones" -- think of bodacious or cretaceous and pluralize them. Botanists have chosen one genus in the given family that is more or less representative and turned it into a -aceae name: for example Aster in the sunflower family Asteraceae. Incidentally, this family used to be called the more descriptive Compositae -- the composites -- because the flower heads are actually composites made up of numerous tiny disc and ray flowers. Several other families have changed name fairly recently (within my life time, at least):
Now anyone thinking scientific names are somehow more consistent or fixed in stone will be rudely surprised. Botanists delight in changing names. Granted they do it systematically, and there will never be two different species -- future, present, or past -- with the same genus and species names. So it is definitely less ambiguous than common names. But, come on! For example, they changed "phylum" to "division" for no apparent reason. As discussed above they changed half a dozen family names just because they're anal. And now with the flood of new genetic and molecular data, they're rearranging the phylogenetic tree completely. Genera, families, and orders are being combined and split apart left and right. And there are all kinds of new hierarchical levels: the old Kingdom, Phylum, Class, Order, Family, Genus, Species business you learned in high-school is just the bare skeleton now-a-days.
(Check out Michael Charter's page as well: California Plant Names: his is much more formal (and probably more complete!) and includes cool biographies of famous botanists and such as well.)