Ah so cool. Chinatown is so tasty. SF china town in particular is a lot more friendly then most so don't be afraid to ask restaurant chefs/waiters and locals what it is you're eating. First off, start walking around the grocery stores and googling the items. Same with items on restaurant dishes/ingredients. It help build up your knowledge slowly over time.
I'm also going to go against traditional advice of recommending 'every grain of rice'. I'm going to recommend "the complete book of japanese cooking" by emi kazuku which is sold commonly in used bookstores and online for like $3. It has a visual index of common ingredients in Asian groceries and essential Japanese pantry items along with great intro recipes.
I also found this. The Asian Grocery Store Demystified. I haven't read this but its an illustrated guide on the top 400 most common ingredients, what region/culinary tradition they are from, and how to use them. Looks pretty useful.