Hi, I want to build a website from scratch without using a CMS or WordPress. I have used both methods before and it is very easy to add a “Find Us On Facebook” plug-in. But I have not done this before with a hand-coded website.
What will I need to get started? I have installed WAMP on my desktop because I believe I will need PHP for this. The ideal things that I am looking for are a Twitter Feed plug-in, Facebook “Like” plug-in and Vimeo or Youtube video support.
Just go to face book and go to social plugins they have very good tutorials! 
All the services you mentioned have their own api and should provide you with a code snippet which you can just copy and paste to your code. You can also go for something like addthis.com
You could also use this http://www.sharethis.com
and as digital apex said, the various services have their own API. Here is a link to facebook’s for their “like” button https://developers.facebook.com/docs/reference/plugins/like/
In online you can get number of sites,which are available according to your need.you can check in ‘addthis’ site,it may be useful to you.
Well you say “follow me”. So all you want and need is a img with a link to your facebook page. if you want to alllow leople to share yoir site then, I have always used addthis. But recently it stopped my page loading in ie8 and they would not even respond to me. So I removed it. I was flirting with different ways to add custom social icons on to my site when I discovered using AddToAny (now Lockerz) you can just pop in your own img in the anchor and it will use your I icon. It’s actually much faster than addthis and offers many more customizations.
dont depend your site on plugin as much as you can do it manually. make social plugin for facebook is very easy. go to this link https://developers.facebook.com/docs/reference/plugins/like-box/ then costumize your box. anda copy the code given to your web page. its so simple.