It depends on the genre you are picking. I'd like to help from the start so I'm going to list down the useful sites we use in general:
AniDB - This is your information site on who-subbed-what with detailed information on videos. Not like you would understand it, but you'll get the general idea if you skim through one series for a few minutes on that site. ANN - Up-to-date news on everything out there that involves the 'Anime' world. BBT - Releases completed series/seasons with the best or good quality from fansub groups.
For programs that are required:
CCCP - Get rid of any third party codec program, including VLC (it's shit) and install this. Use the MPC inside of it. There are three other steps I want to put down here but I'll list them later if you do take this step. They're optional, but they'll make the player lighter and the subs will be smoother and easier to load. uTorrent 3.0 - This is the best uTorrent version that doesn't have all the crap they put in the later versions, including ads ... unless you want ads then go download the latest version. Disable the 'update to newer version' in General tab.
Though I gave you the break down of how I do things (and the majority of us), you can also go to Funimation or Crunchyroll and stick to their streaming services which is several steps below the fansub quality you get.
As far as getting into the Anime world ... the links provided by The Major is a good start. It all depends on what you're into. Are you into mo'e (cute) anime? Realistic? Fantasy? Dark Fantasy? And so on and forth.
But here's one other thing you could use - go to AniDB, click on 'Calendar', in the drop down box where it lists the months, scroll down to the 'seasons' and you will see all the anime releasing/released for that season and for the year you picked. I use that for quick reference to what I missed, what's coming up soon, or what I want to watch.