Web Analytics 2.0: The Art of Online Accountability and Science of Customer Centricity. I understand this is a weird suggestion but it trains you to think of business as defined and measurable goals. This is a very powerful concept when chasing profit. http://www.amazon.co.uk/Web-Analytics-2-0-Accountability-Centricity/dp/0470529393
This one is a classic :
It is a bit more oriented towards bigger businesses than Startups but it helps you having the right mindset to generate impact for sure.
Read Web Analytics 2.0 by Avinash Kaushik
Avinash was/is an analytics evangelist for Google and used to head analytics at Intuit. The book will give you a great grounding in online measurement and has examples of a bunch of reports.
I'd also grab a copy of the Excel Bible for whatever year you're using. It gives you scenarios for using different functions and macros and examples of everything.
All the analytics packages have training you can take, just look around their sites.
As a data analyst myself, yeah, it is exceptionally hard to become a data scientist without the master's. I work with a few analysts who definitely are skilled enough that they should be scientists, but most companies will not promote an analyst to scientist without an advanced degree, which sucks. I'm still learning the data science end to become more effective, but honestly, data analytics is a broad field and in my experience, brings you closer to the business and product testing side of things than data scientists tend to get. I find the data analyst side exciting because I love to see how end users interact with the final product.
Someone else mentioned SQL and Excel being the building blocks of a data analyst's toolset. I'd add to that Google Analytics (you can use the free version and just hook it into a website), Google Adwords, Facebook Analytics, Tableau, and PowerPoint/presentation skills. You can try all of those for free, and it gets you a glimpse into how websites and e-businesses collect data on the back end that you can later report on. Having a head start on understanding campaign tracking and how to report trended data will be huge in your favor. Also, on Excel, definitely master the v-lookup and Pivot table functions, which I swear I use on a daily basis.
Additionally, if you know what field you want to work in, you really need to keep up on the news in the field and build up some industry knowledge. I work in the music industry now, so it is a lot of HypeBot and other music/tech sites. When I interviewed for my present job, having industry knowledge of Spotify vs. Pandora offerings or the advertisement model on ITunes Radio comes across as you speak to the people you are interviewing with, and they become more convinced that you have the knowledge and passion to succeed. Passion counts for a lot, especially if you are short on experience or fighting against other entry level applicants. The presentation skills help you convey yourself and will give you an interviewing edge.
Edit: here is a book that helped me a lot when I was brand new to the field. It can help you understand the jargon used in web analysis specifically, and give you ideas on how to build up your career in data: http://www.amazon.com/Web-Analytics-2-0-Accountability-Centricity/dp/0470529393