Short answer
Through Allah's mercy, by dying with faith and doing good deeds. Whoever dies believing there is no god but Allah will enter Jannah in the end, and good deeds raise a person's rank in it. The Prophet ﷺ said no one enters Paradise by his deeds alone, only by Allah's mercy.
Entry into Jannah is by Allah's grace, and its condition is dying with iman. Deeds are not the price of Jannah, but they are the way Allah has made to it and they decide a person's rank; sins may delay a believer's entry unless Allah forgives.
The four schools agree on this.
Explanation
The Quran pairs the two again and again: "those who believe and do righteous deeds" will have gardens beneath which rivers flow (2:25). Surah al-Asr says all people are in loss except those who believe, do good, and advise each other to truth and patience (103:1-3). Faith is the foundation; deeds are what you build on it.
The Prophet ﷺ said: "Whoever dies knowing that there is no god but Allah will enter Paradise." He also said that no one's deeds will admit him to Paradise. The Companions asked, "Not even you?" He said, "Not even me, unless Allah covers me with His mercy." So no one earns Jannah like a wage. Our deeds are small next to Allah's blessings, and Jannah is His gift.
Why do deeds matter then? Because Allah made them the means of His mercy, and the Quran says people enter Jannah "for what you used to do". Deeds decide your rank, and sins may lead to punishment first. Sunni creed holds that some sinful believers may be punished in Hell for a time before they enter Jannah, unless Allah forgives them or someone intercedes for them by His permission. See Will Muslims stay in Hell forever?
In practice: hold firmly to tawheed, keep the five daily prayers, fulfil the rights of Allah and of people, repent often and never despair of Allah's mercy. Hasten to forgiveness from your Lord and a garden as wide as the heavens and the earth (3:133). Read about what awaits in Jannah in Islam.
The evidence
Quran, Surah Al-Baqara 2:25
وَبَشِّرِ ٱلَّذِينَ ءَامَنُوا۟ وَعَمِلُوا۟ ٱلصَّٰلِحَٰتِ أَنَّ لَهُمْ جَنَّٰتٍۢ تَجْرِى مِن تَحْتِهَا ٱلْأَنْهَٰرُ ۖ كُلَّمَا رُزِقُوا۟ مِنْهَا مِن ثَمَرَةٍۢ رِّزْقًۭا ۙ قَالُوا۟ هَٰذَا ٱلَّذِى رُزِقْنَا مِن قَبْلُ ۖ وَأُتُوا۟ بِهِۦ مُتَشَٰبِهًۭا ۖ وَلَهُمْ فِيهَآ أَزْوَٰجٌۭ مُّطَهَّرَةٌۭ ۖ وَهُمْ فِيهَا خَٰلِدُونَ ﴿٢٥﴾
And give good tidings to those who believe and do righteous deeds that they will have gardens [in Paradise] beneath which rivers flow. Whenever they are provided with a provision of fruit therefrom, they will say, "This is what we were provided with before." And it is given to them in likeness. And they will have therein purified spouses, and they will abide therein eternally.
Faith and good deeds lead to Jannah.
Quran, Surah Al-Asr 103:1-3
بِسْمِ ٱللَّهِ ٱلرَّحْمَٰنِ ٱلرَّحِيمِ وَٱلْعَصْرِ ﴿١﴾ إِنَّ ٱلْإِنسَٰنَ لَفِى خُسْرٍ ﴿٢﴾ إِلَّا ٱلَّذِينَ ءَامَنُوا۟ وَعَمِلُوا۟ ٱلصَّٰلِحَٰتِ وَتَوَاصَوْا۟ بِٱلْحَقِّ وَتَوَاصَوْا۟ بِٱلصَّبْرِ ﴿٣﴾
By time, Indeed, mankind is in loss, Except for those who have believed and done righteous deeds and advised each other to truth and advised each other to patience.
Success depends on faith, good deeds and mutual advice.
Quran, Surah Aal-i-Imraan 3:133
۞ وَسَارِعُوٓا۟ إِلَىٰ مَغْفِرَةٍۢ مِّن رَّبِّكُمْ وَجَنَّةٍ عَرْضُهَا ٱلسَّمَٰوَٰتُ وَٱلْأَرْضُ أُعِدَّتْ لِلْمُتَّقِينَ ﴿١٣٣﴾
And hasten to forgiveness from your Lord and a garden as wide as the heavens and earth, prepared for the righteous
Urges believers to rush to forgiveness and Jannah.
Sahih Muslim 26
Sahih... مَنْ مَاتَ وَهُوَ يَعْلَمُ أَنَّهُ لاَ إِلَهَ إِلاَّ اللَّهُ دَخَلَ الْجَنَّةَ ...
"Whoever dies knowing that there is no god but Allah will enter Paradise."
Dying on tawheed is the condition for entering Jannah.
Sahih al-Bukhari 5673
Sahih... لَنْ يُدْخِلَ أَحَدًا عَمَلُهُ الْجَنَّةَ ...
"No one's deeds will admit him to Paradise, not even me, unless Allah covers me with His grace and mercy."
Jannah is entered by Allah's mercy, not bought by deeds.
Where the ruling is recorded
- al-Aqida al-Tahawiyya, Section on Paradise and Hell and the people of the qibla. States that believers who sinned are under Allah's will and will be brought to Paradise by His mercy.
- al-Fiqh al-Akbar (Imam Abu Hanifa), Section on reward and punishment. Affirms that reward is from Allah's grace and punishment from His justice.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.