If you have no idea about anything game related, then this is a good place to start. Here I will lay out EVERYTHING.
First off there are three major brands in the industry: Nintendo, Sony, and Microsoft. Each company has a home console, Nintendo has the Nintendo Wii (Wii for short), Sony has the Playstation 3 (PS3), and Microsoft has the Xbox360(Xbox360). Nintendo also has the portable systems the Ninendo DS (DS) and Nintendo 3DS (3DS) out, and Sony also has the portable system Playstation Portable (PSP).
Each company has their own controller and user interface, but all of them are pretty easy to learn after a couple of uses. Though there are many systems out there how do you know which one to get? Well the cliche is that the Nintendo company (selling the Wii, DS, and 3DS) appeals to people of all ages, while the PS3, PSP and Xbox360 appeal to the older audience. Well Nintendo games do appeal to people of all audiences (because there are so many of them) and their systems have more interactivity with the Wiimote (the controller you use for it), and the touch screens for the DS systems, but the PS3 and Xbox 360 has other games that can appeal to all audiences, it just depends what games you like and if there are certain games you follow (meaning you are a fan of the series who likes to buy all, or most of the games relating to that series or character.)
Another feature that has just started with this generation is that you can do other tasks on your system other than just playing video games. You can download games online (for a cost of course) download music, videos and other things (it varies by system and again more costs, but sometimes worth it)
So your thinking "Well that all sounds good, but I don't have that much money" Well here's the thing neither do I. Here is the breakdown for the pricing on the systems:
Wii: $200 plus tax
PS3: $250+ plus tax
Xbox 360: $200+
Nintendo DS: $130+
Nintendo 3DS: $250+
PSP: $130+
For the Xbox360 and PS3 most of the time your paying for how big the hard drive is, so you will want to consider how much you will use the system before choosing. The DS, 3DS, and PSP is also about hard drive and interface which leads me to my next point, games:
Wii games and Xbox360 games cost $50 when they come out, PS3 games cost $60 when they come out, DS games cost $35 when they come out, and 3DS and PSP games cost $40 when they come out. But games go down in price as they get older, so it may be a good idea when starting out to buy some low cost games to find the genres and series you like.
Next point genres there are many genres from party games, and music games, to fantasy role playing games and shooter games. I encourage you to ask around to find and try different genres so you know what you like and you don't end up wasting money on games you don't like.
I end with these two pieces of advise, first DO YOUR RESEARCH. Before buying ANYTHING look online, in magazines, and what ever else you can think of. A lot of times they will help you find the games and systems that are right for you. Last piece of advice BE THE DECIDING FACTOR IN ANY DECISION. I have bought countless games, and for a while all I would do was listen to reviews, but then I got a game, rated very highly, and guess what it was TERRIBLE so ever since then I always look at every aspect of a game before buying it.
Well that should be enough to get you started so good luck and happy gaming.