http://builtwith.com as John mentioned earlier is your first step, and as others mentioned if you are just beginning go with WordPress, about a third of all new sites now are on WordPress so you have the support, security and flexibility that goes with that.

If you're looking at a WordPress site you like the features of, you can dig a little deeper with http://www.wpthemedetector.com/ to see the theme they use and often the plugins they use. In my experience it only recognizes about 30% of the plugins out there, but often you'll get some great insights into how a site has been put together, and Viktor's tips above will help you find even more.

join.me and teamviewer are two I use. Teamviewer if you don't want someone to have to be sitting there to "let you in", they just authorize you and you can log in any time. Great for accessing your own computer while away.