The linked guide that Arremer posted here is absolutely awesome, but it's probably a bit much for a very new player. When I teach new players I gave them 8 good ward spots to use- some more basic than others. I've circled them on the image linked:
- First, there are the two obvious ward spots near the runes. These are your default spots, and they're thus the most likely to be counterwarded. You should use others if you start getting counterwarded.
- Next, there are the wards which block the pull camps. Blocking these should be done almost automatically in every game with the first set of wards bought. These are the circled spots in the image with the pink lines coming from them, which indicate the blocked camp. They can be a bit tricky to place, so try it out in a practice game.
- Finally, there are 4 offensive ward spots. These are more situational in their use, but they're also the most important to allow you to take advantage of your team being ahead. If you don't ward offensively when you have a lead, you're inviting the other team back into the game. The yellow spots are the most well known, but the other two spots are nearly as good.
There is so much to warding that it's something you'll improve at for a very long time. For a complete new player, these are where I'd suggest starting.
So an overview: with your 2 wards at the start place one that's able to see a rune location, and one to block the pull camp. Try to do this right around 0:00, but not before, so that your mid hero is able to see where the 6:00 rune spawns. (Observer Wards last 6 minutes). This is pretty important. From there, keep wards up in the middle and maybe place aggressive wards if you know you can do so safely. Mostly you're concerned with keeping an eye on gank attempts and Roshan in the midgame. After you take T2 towers with your team, worry about getting offensive wards placed after you win teamfights. This will let you secure the game. Good support players are way more influential in Dota2 than they are in LoL, but it's still the same thankless role and much harder to accomplish.
I suggest you read my reply here too to know how to understand counterwarding, which is done with blue Sentry Wards (they last 3 minutes).
Good luck, any questions feel free to reply.