Depends on your goal. Lots of people start with "Build your own website the right way" and an idiots or dummies guide to wordpress. With those two basics and great salesmenship you can get started.
I would say I am pretty good in HTML & CSS, and I am just starting to get into PHP now. My Photoshop skills are basic enough, so I wouldn't class myself as much of a designer. I think I would be looking more into the coding end of things. Should be starting an Internship very soon, so wanted to get someone's perspective on it.
A Web designer and developer must be aware with the fundamentals and be technically well versed with designing and development. They should be conversant with HTML and CSS and these will assist them build a customized web site design and development. The designer should have complete knowledge of the powerful design tools as Adobe Photoshop and Dreamweaver as well as he has to be creative and have the knack of using color and shapes appropriately. He/She should be aware of all basic coding and connectivity. It is a requirement to refer to the latest tutorials and update and improve and enhance skill.
When you say starting out, it will vary then. The basics, with regards to tools - Photoshop/Fireworks for design. A text editor from Notepad to Sublime to Dreamweaver. Knowledge of basic usage of database tools like SequelPro (Mac) or something similar - just to do minor DB maintenance of backing up/exporting/importing etc.
As for head knowledge - HTML, CSS, working knowledge of Java script. For design, basic design principles. Still a good read is The Principles of Graphic Design. You probably want some definition and draw the line somewhere as to which way you are leaning - designer/developer or developer/okay designer. Whichever you choose you can always pick up the other one a little later.
....For a Web Designer/Developer starting out, what are the basics that they would need to know?
How to grab the attention of prospective clients, turn the attention into interest, and finally how to to separate their wants from their needs in order to offer a valid and valuable solution.
All the design knowledge in the world is not going to sustain your business if you don't learn how to deal with (prospective) clients in a mutually profitable way.
Web Designing or development is a hybrid of Creative and programming skills.In the first phase of web designing you will create web graphics using various tools such as Photoshop, Illustrator,Flash and Corel Draw.In the second phase,The development you will program the web pages using java script,PHP,Ajax and ultimately host the site in the server.The right blend of web graphics and development makes a wonderful website .
As a few have already pointed out the skill set is broad, if you are going to work alone then you need a much wider range of skills not only for web design but also how to get clients and run a business. If you find work at another company you should look at becoming an expert in a specific set of skills.
I agree with most of what William has said but disagree about knowing flash as being a pre-requisite, it is just not generally accessible enough.
I think the key thing to remember is that you need to start somewhere for me the basics are:
Server side scripting language (e.g. PHP) and associated database
Content strategy - with SEO as a subset of knowledge
Basic design principles, I absolutely love the 1st edition of the Principles of Beautiful Web design published by Sitepoint.
Principles of accessibility, a good place to start is on the Nielson Norman group website.