How do I start a Web-Analysis?

I would start here:
http://blog.kissmetrics.com/startup-analytics

Then I would read anything else that sounds interesting here:
http://blog.kissmetrics.com

More importantly, *why* do you "have to analyze a website and the related Facebook page"? Lets say you have the perfect data, what are you planning to do with it? What are you trying to change?

I agree with the previous answer that Google Analytics and the built-in Facebook stats are a great place to start for this. One question to ask is what the goals are for the business. If your goals are to increase Facebook page likes (which usually isn't a top recommendation), then your reporting will be different than if your goal is to get people to your site to order a product (a much better way to use Facebook).

It's difficult to say which key figures to use without know more about the business. The top ones are traffic, traffic sources, and conversions (if you have goals set up in Google Analytics). If you don't have enough traffic, then you need to focus on generating that, and if you are getting enough traffic but aren't converting, then you need to work on improving conversion rates. The good news is that all of this can be done with Google Analytics so long as you have it set up properly.

Expertise in both digital marketing and web analytics. I have experiences working with multinational brands on their web report analysis and marketing effectiveness.

Goes without say GA is the best free tool available.

Here's the general process I recommend:
1. Understand business goals and objectives - who is this report prepped for and for what purpose? what kind of website is it?

2. GA Audit & Setup - most people ignore this step but its actually very critical because if you find out the site is not tracking critical information, any data you pull from it will be skewed and unreliable.

3. Determine KPI which addresses your objectives. - different objectives will result in the need for various KPI. But in general, conversions and transactions are always on the list.

4. Digging into data to find insights. - using segmentation & filters to gather specific data which can provide very specific insights. (too often people fall into the trap of high level KPI which offer little insight or actionable next steps)

I'd be more than happy to hop on a call to help you figure out these targets and work through.