If you look closely at the F and J keys on any normal keyboard (assuming you're using an English language keyboard), you should find that they have a little bump on them. The bumps are there to help you find those keys without looking at them - they allow you to type in the dark as you can simply feel for them with your fingers, and the idea is that your index fingers should normally rest on those keys. (If you don't know which fingers your index fingers are, let me explain what the word "index" means: it sounds like a really fancy word, but it's simply related to the Latin for "indicate", or "point" - your index fingers are the ones that you point with. The index of a book is a section which indicates where you can find what you're looking for by pointing you to particular pages.)
Having worked out which keys your index fingers should rest on, your other fingers should automatically find themselves resting on the A, S and D keys - that's with your left hand - and the K, L and ; keys for the right. To type any of the letters a, s, d, f, j, k or l, all you have to do is press down with whichever finger is already resting on that key. All the other letter keys should be pressed by the finger nearest to them, so the finger used for the A key will also be used for the Q and Z keys. The finger used for F is also used for R and V, but it's also used for T, G and B because there is no finger resting on the G key. In the same way, the finger on the J key is used for U and M as well, plus Y, H and N.
The keyboard layout comes from mechanical typewriters which had to put columns of keys in at an angle in order to keep all the levers apart at equal distances underneath, and sadly this awkward design is still in use today even though the levers have completely disappeared: we still have sloping columns of keys which make typing a lot more difficult than it should be. I wish keyboard manufacturers would give us the option of sliding the whole QWERTY row a little to the right and the whole ZXCVB row a little to the left, but progress is often slow when people get stuck in their ways: there are alternative schemes for arranging the letters on the keyboard which have been carefully designed to make typing easier, but they're all stuck with the same sloping columns. When you need to type a number key it's hard to hit the target without looking because you've always got to aim a long way to the left of where it really ought to be, but you don't really need to worry too much about the numbers - just concentrate on typing the letter keys with the correct fingers and try to get up to a reasonable speed. To save you from looking for it, the comma (,) can be thought of as a komma (spelt with a K) - use the same finger as used for the letter K. The full stop (also known as a period) should be pressed with the finger which rests on L, and you can remember this by thinking of the word "last" - it's the last key you press at the end of a sentence.
So, if you put your index fingers on the F and J keys, it should be obvious which finger to use for all the other letter keys, and don't allow any finger to be lazy - P should be typed with the little finger of your right hand, and so should the apostrophe ('). The little fingers should also be used to hold down the shift keys for typing capital letters (shift keys usually have fat arrows on them which point upwards), and if one hand's typing a letter that needs to be a capital, the little finger of the other hand is the one that should be holding down one of the shift keys. There are lots of exercises that people are made to do in typing classes where they spend hours typing really boring stuff, but if you force yourself to use the correct fingers for all the keys, you should be able to give those tedious classes a miss by learning to type while writing things that actually matter to you. Just force yourself not to be lazy - make sure those little fingers are pulling their weight.