My LED toggeling doesn't work the way I want
There are a few problems with your approach.  


You seem to have the button backwards.  You should wire a button so that it is between the pin and ground.  This way it should read LOW when pressed, not HIGH.  It should also have pinMode(pin, INPUT_PULLUP) instead of INPUT.  With the button wired the way you have it to read HIGH then you will need an extra resistor for each button.  With it wired the right way where it reads LOW then it needs nothing extra. 
If the first if statement is true and the button is pressed and it turns on the led, what do you think are the chances that you are fast enough to get your finger off the button in the 62.5 nanoseconds it takes to get to that next if statement?   It's not going to happen, so the button is still pressed there and now the led is on so this line turns it right back off.  Only in the rare case where you happen to get your finger off the button at just the right instant will the led stay lit.  To solve this, look at the "State Change Example" that comes with the IDE.  It shows how to keep track of the last state of the button in a variable so you can act only once when the button actually changes state.  
Once you get that worked out you will notice that it seems like for every time you press your button it registers tens of presses.  This is switch bounce.  That's a term you should google.  The contacts are making and breaking contact really fast in the in-between pushed and not-pushed state.  But you need to get the first two issues solved before you worry about bounce.