If you don't feel totally confident then definitely pick up Head First HTML. Aside from that there are a few websites I would recommend:
A List Apart,
Stop Design
and as others mentioned the W3 website.
Working with a designer often means that they will produce mockups using Photoshop and you will in tern work off those. As that is the case having a working knowledge of Photoshop will be very useful for you. You don't have to be a wizard but some basic knowledge will enable you to do things like create image sprites from the mockup and get information relating to the width, height, color, etc of the different components in the design. As far as getting up to speed quickly there are many books on the subject, the Photoshop One on One books are a pretty good series and there are video tutorials available at Lynda.com.