Describing SharePoint as a 'website' is like describing the Grand Canyon as a drainage ditch. SharePoint is a huge product and while, yes, it does do websites, that is really only about 5% of what it actually does.
The launching point for all of the research you will need is probably the Microsoft documentation itself. There is a lot of it here though and it is often written using language that assumes extensive familiarity with SharePoint.
The first place focus is to identify the intended audience for the site. If it is exclusively internal users located behind the firewall then you are likely looking for an 'On Premise' solution, which means you need to download and install it on a rather powerful server with a solid database server backing it up.
However, if the audience is mixed between internal and external or is almost exclusively external, then you are in luck as Microsoft offers SharePoint 2013 in the cloud which really makes life much, much easier for someone new to the SharePoint world.
Microsoft has detailed documentation comparing On-Premises and Hosted options though a much shorter summary is available. The choice between On Premises or Hosted will likely dictate many of your other choices so this should be addressed first.
If you are looking to just jump in and play with SharePoint, you can install it by downloading the bits from MSDN and then following these instructions. However, to get started immediately, you can sign up for the Preview and play around there, usually in less than 15 minutes!
If you end up deciding that you need an on-premise installation of SharePoint, I would strongly recommend that you bring in a qualified SharePoint Consultant to handle that task. There are a lot of variables that go into properly setting up a SharePoint farm and any one of those could put your farm (and data) at risk. Beyond that is the fact that SharePoint is not meant to stand-alone. It is designed to integrate with SQL, Active Directory, Exchange, Office, etc., and each of those touchpoints will also need to be handled.
The absolute best resource for SharePoint related questions is the SharePoint community itself as members of the community generally have detailed blogs that break down behaviors and functionality into easily understandable bits. Odds are that if you are struggling with something then someone somewhere has detailed steps on how to get past that bit.
Expect to learn a lot on this road and expect to keep learning for years.