I will try and keep it as simple as possible -
Backlinks - Are the links that other sites link to yours i.e. you are getting site traffic from other sites. The bigger and better the other site is, linking back to yours, the better opportunity you have to rank higher in Google or other search engines. There are heaps of spammers which offer backlinks for free or for link exchange program, stay away from them. Find genuine sites, more importantly sites related to your topic for backlinks, journals, articles, blogs, forums can offer good quality backlinks.
Index by Google - Sign up to Google and use their products - webmasters tool to submit your site and to index it i.e. you are sort of publishing your webpage on search engines, analytics tool to keep a track of visitors to your site and get insights on what pages/content is popular on your site, geographical location of visitors, etc, adwords tool to create online campaigns for marketing or selling products and services, create online ads which will be displayed by Google and/or other search engines or networks. These are the common products you can use via Google however for others to know and search engine bots to know that your site exists, you have to submit your site to Google or Bing or AOL or any other search engines.
Where and how to find good dropped domains - Unfortunately, i can not answer that specifically as i do not concentrate on that area.
How to know good domain - Well its a very broad question and to be honest i really doubt there is anyone who can answer that point to point because for one the domain name might be outstanding but for other it might have zero value. There are domains which doesn't make any sense but are being sold for hundreds and thousands of dollars and there are some which do make sense but seem to have no favourites. In a general opinion, short, good keyword, catchy domains work but its up to end users discretion and its not entirely a domain name that works, its the work behind the domain name to make it a brand that works. Hypothetically, few years ago one would have thought what sort of name is Google, Yelp, Youtube, and there would be many more which would have made no sense back then but the work that went behind that domain name to make it a brand is something really valuable now.
How to transfer domain to end user - All you need is the registry key, a key assigned to each domain name. If you have the registry key for a domain, you can transfer the domain hassle free from one registrar to other.