The best way to learn to play the piano is, like most other things, practicing it daily or at least regularly. It is good to initially practice scales and chord cadences. To put your right hand in the position to play the C-G notes, put your fingers on the keyboard in the order shown in the image below:
You should memorize the notes in relation to black keys: B is not the seventh key from C, but it's the key on right side of the three black keys. Additionally, you should sit at the front of the bench (or chair, although it is recommended for you to get a piano bench or something that resembles it) and place the middle c key right in front of your bellybutton. The middle c key in the keyboards containing 61 keys is the white key after 3 sets of black keys (meaning that you'll count ten black keys starting from the left and put the white key right before the black one to the right in front of your navel) For regular pianos (88 keys), add an extra 6 black keys to the set of ten.
Sit down and play around for a bit; experiment, have fun. (Keep your wrists straight and relaxed.) It's best to have a real piano for this, but if one isn't available, at least make sure the keyboard you're using has touch sensitivity.
Your wrists should be straight and but your hand should be relaxed. Let your arm fall to your side, relaxed and parallel to the keys. Make your hand into a fist and then extend your fingers straight. Then relax and let your fingers fall. The result is the correct hand position. Of course this is only the starting position, in real playing it immediately flies out of the window. A relaxed hand has fingers that are slightly curved, a bit like how a hand looks resting over a computer mouse. This will allow you to play the black and white keys easily. The first things you'll probably notice (if you don't know already) is that keys on the left are low, and keys on the right are high; also that playing two adjacent keys simultaneously sounds dissonant.
The number of keys may seem overwhelming at first, but their organization is simple -- they're in a repeating pattern of octaves, one of which is pictured above. Try finding one of the C notes in the middle of the keyboard. Now play another C above or below it -- you'll hear immediately why they have the same name.
The black keys are chromatic notes and used when the key requires notes that sound 'in-between' what you get when playing on the white keys.