If you're not feeling completely confident, picking up Head First HTML is a great place to start. Additionally, I recommend checking out some websites like:
A List Apart,
Stop Design,
and of course, the W3 website as others have mentioned.
When working with a designer, they may provide mockups using Photoshop for you to work off of. Having a basic knowledge of Photoshop can be very beneficial in this case. You don't need to be an expert, but understanding how to create image sprites from mockups and gather information on dimensions, colors, etc., can be helpful. To quickly get up to speed, there are plenty of resources available such as the Photoshop One on One series from O'Reilly books and video tutorials on sites like Lynda.com.