When you first try to play anything fast it is quite likely to be both uneven (random variations in the volumes of notes) and unsteady (random inaccuracies in the durations of notes).
Let us take, for example, the first of Hanon's exercises.
Hanon 1 Braille
The very first stage of preparing this is to practise it slowly, listening carefully to check that the notes are even and steady at an easy tempo. During this stage, as in all the steps that follow, monitor your hand for signs of tension. It is essential that the hand should feel relaxed if real agility is to be achieved.
You should discuss this with your teacher and work on exercises together.
Valuable though it is, no amount of slow practice will enable you to play this exercise at speed. The secret of playing a passage such as this up to speed, both evenly and steadily, is to make sure that every individual movement has been practiced up to tempo. But this cannot be done all at once. What is needed is a strategy for practising just some of the movements up to speed and then resting the hand.
This can be achieved using the following steps:
Step 1
This practises the movements between successive pairs of notes, up to speed. The hand is able to rest after each little burst of speed. Make sure that the hand relaxes completely before proceeding on to the next fast pair of notes.
Step 1 Braille example
Step 2
In this step the movements that were not practised up to tempo in Step 1 are now practised up to speed.
Step 2 Braille example
Step 3
In step 3 most of the movements are practised up to tempo. It should be possible to play this once Steps 1 and 2 have been thoroughly practised. The notes on which you rest should allow the hand to release any unwanted tensions before carrying on. Note that the movements from the thumb and from the 5th are not practiced up to speed in this step.
etc.
Step 3 Braille example
Step 4
This step is almost the same as Step 3 except that every movement is practised up to speed, including the movements from the thumb and 5th.
Step 4 Braille example
Note the simple principles behind this practice strategy:
[1] the hand is given places to relax after each burst of speed
[2] the bursts of speed are made progressively longer
Step 5
A logical continuation of this strategy is, therefore, to lengthen the burst of speed even further. In this step the whole pattern of the exercise is practised and the hand is rested on the thumb note. Notice that the thumb note is then played again in order to practise quickly the movement from thumb to 2nd.
Step 5 Braille example
Step 6
So far the hand has always rested on the first note of the pattern. Even if it then starts the pattern again up to speed, as in Step 5, it has not had the practice of flowing from one transposition of the pattern to the next. Step 6 is designed to practice this before even longer bursts of speed are attempted.
Step 6 Braille example
Step 7
Here the burst of speed is two bars long - we see two iterations of the pattern before the hand is rested.
From here on we simply carry on progressively increasing the length of the burst of speed. The crucial thing is to ensure that, after each burst of speed, any tension in the hand is released completely.
Step 7 Braille example
And remember:
[1] In the rest phases of each step make sure that all tension is released before you continue. You may rest on these notes for as long as is necessary.
[2] Listen closely all the time to the sounds that you are making. Are they even and steady? The above steps should help to make them so.