I was like you when i newly started to high school. And i had asked my teacher who was typing without looking at the keyboard how to do it. He had given me some tips, and i learnt it in just 2-3 months. The essential point is, you must always put your fingers above the buttons. I have a Q keyboard so i will explain it by giving example from my keyboard :
In most Q keyboards, there is a small sign on F, J and numpad 5 buttons, these signs are for the blind people to align their fingers by finding it and associating the index finger with those signs. ==>
Placement of the fingers :
So, to get access to all other buttons by using your all fingers, associate your index fingers with F and J buttons. And now, align your other fingers according to the order, your middle fingers above D and K, your ring fingers above S and L, and, your little fingers above A, and the button next to L (so that you can easily access to P button, dots etc.) About the thumbs, both will be placed above the space button (thumb on your left hand will stand above the left corner of the space button, and the one on the right will stand above the right corner of the button).
Starting to type ! :
Now, when it comes to type, you will start by repeating small sentences. Like, "I am a student.". To type it fast, the first finger which you will move will be the finger which is the nearest to the I button. In my case (Q), it's my middle finger (right hand).
So, move your middle finger above that key, and press I, and as soon as you pressed it, move it back to it's own place, K button. Now, press Space by using both of your thumbs (i am not using both, i am using only left thumb, depends on how you prefer),
for A button, use your left little finger,
for M, use your right index finger,
for T button, use your left index finger,
(Important), for U button, use your left middle finger, even if your right index finger is nearer, because your middle finger is longer than your index finger, so that it will be easier for you.
for N button, use your right index finger.
That's how you use all of your fingers. Keep repeating this exercise everyday, and each 3 days, make a longer sentence. At the end of 2nd or 3rd month, you will be extremely faster according to the past.
Speed exercises ! :
A) Left hand
When you are in class in front of your pc for example, if you are idle waiting for your teacher to do something etc, open a notepad somewhere, hide your right hand behind your back, and with your left hand, keep typing "yeah". This word is writable with only left hand :
Index finger for Y button,
Middle finger for E button,
Little finger for A button,
Index finger for H button.
Keep doing this and each time you finish typing "yeah", press space by using left thumb. And when you typed too much that will draw others' attention, again, keep your right hand hidden, and move your little finger to left CTRL, and move your ring finger to A finger. So you can easily do CTRL + A, and if you press 1 more key, it will delete all the spams. This way will allow you to gain speed on your left hand.
B) Right hand
Type "jokin lookin ok" repeatedly without doing anything with your left hand (keep it above ctrl+a in case you need to delete all). This will increase your right hand's movement speed if you start to do this frequently :
Index finger for J,
Ring finger for O,
Middle finger for K and I,
Index finger for N,
(press space with right thumb finger)
Ring finger for L,O,O,
Middle finger for K, and I,
Index finger for N,
(press space with right thumb finger)
Ring finger for O,
Middle finger for K.
You can create your own exercise words and increase your hand with them too.
Good luck.