The body without a heart is useless. The Prophet (peace be upon him) has said:
There is a piece of flesh in the body if it becomes good (reformed) the whole body becomes good but if it gets spoiled, the whole body gets spoiled– and that is the heart. (Al-Bukhari)
There are three stages of the heart:
Corrupting Hearts
The heart is corrupted by committing acts of sins or disbelief. The Prophet said:
When a slave (a person) commits a sin (an evil deed) a black dot is dotted on his heart.
There are some sins which we are not aware of committing that leave spots on our heart, and these are the ones which we should be most watchful of.
A common example is backbiting. It has become so common everywhere that not criticizing someone behind their back might label you as being backdated or unsocial.
Internet social media, blogging, and YouTube have made it especially easy and dangerous, and I have seen people not even sparing scholars, actually thinking they are doing something righteous.
Another common disaster is showing-off, and it is actually a kind of hidden shirk.
Curing Hearts
Tazkiyah (Purification)
He has certainly succeeded who purifies himself. (Quran 87:14)
For curing the heart, it needs to be purified first from all kinds of filth like envy, hypocrisy, arrogance, gluttony and other diseases. First step towards purification is istighfar. The Prophet said:
When a slave (a person) commits a sin (an evil deed) a black dot is dotted on his heart. Then if that person gives up that evil deed (sin), begs Allah to forgive him, and repents, then his heart is cleared (from that heart covering dot); but if he repeats the evil deed (sin), then that covering is increased till his heart is completely covered with it. And this is Ar-Ran that Allah mentioned (in the Quran): Nay! but on their hearts is the Ar-Ran (stain) which they used to earn” (Quran, 83:14). (At-Tirmidhi)
Another form of tazkiyah is charity. The words zakah and tazkiyah come from the same root word, meaning purification. Both zakah and sadaqah are purifying. The Prophet said:
Charity extinguishes sin as water extinguishes fire. (At-Tirmidhi)
Reading and reflecting on the Quran
O mankind, there has come to you instruction from your Lord and healing for what is in the breasts and guidance and mercy for the believers. (Quran 10:57)
Allah calls the Quran shifa , i.e. medicine for hearts. Reciting the Quran itself is purifying even if we don’t understand the meaning. To learn correct recitation, you can have a look at the course Read Quran in 20 hours.
Patience in the face of trials
The Prophet said:
The Fitan (trials, tests) are offered to the hearts, just as the straws that are sewn into a woven mat, one after another. Any heart that accepts the Fitan, then a black dot will be engraved on it. Any heart that rejects the Fitan, then a white dot will be engraved on it. The hearts will therefore become two categories: white, just like the barren rock; no Fitnah shall ever harm this category as long as the heavens and earth still exist. Another category is black, just as the cup that is turned upside down, for this heart does not recognize righteousness or renounce evil. (Muslim)
Dua
There are many duas which you can make. The best dua is of course that which comes from the heart. I’ll give you one beautiful dua each from the Quran and the sunnah.
O Turner of the hearts, make my heart firm in Your deen! (At-Tirmidhi)
Our Lord, let not our hearts deviate after You have guided us and grant us from Yourself mercy. Indeed, You are the Bestower. (Quran 3:8)
There are two excellent books on this topic which you can benefit greatly from: Diseases of the Hearts and their Cures, by Ibn Taymiyyah, and In the Early Hours, by Khurram Murad.
Source: Understand Quran.