How can someone who used to commit adultery and steal repent?

Firstly: 

Adultery (zina) is a major sin. Allaah says (interpretation of the meaning): 

“And come not near to unlawful sex [zina]. Verily, it is a Faahishah (i.e. anything that transgresses its limits: a great sin, and an evil way that leads one to hell unless Allaah Forgives him)”

[al-Isra’ 17:32]

The Prophet (peace and blessings of Allaah be upon him) said: “The adulterer is not a believer at the moment when he is committing adultery; the wine-drinker is not a believer at the moment when he is drinking wine; the thief is not a believer at the moment when he is stealing; the robber is not a believer at the moment when he is robbing and the people are looking on.” (Narrated by al-Bukhaari, 2475; Muslim, 57). 

It is a major sin, and the one who does it is warned of a painful torment. In an important hadeeth – the hadeeth of the Mi’raaj – the Prophet (peace and blessings of Allaah be upon him) said: “We went on and we came to something like a tannoor oven.” I [the narrator] think that he said, that in it there were shouting and voices. “We looked inside and we saw naked men and women, towards whom flames were coming from the bottom of the oven. When the flames reached them they made a noise. I said to them [the two angels], ‘Who are these people?’ … They said to me, ‘We will tell you… the naked men and women in the structure like a tannoor oven are the adulterers and adulteresses.” (Narrated by al-Bukhaari in Baab Ithm al-Zunaat, no. 7047). 

Allaah also punishes the adulterers severely in this world, and has prescribed the hadd punishment for that. Allaah says concerning the unmarried person who commits zina: 

“The fornicatress and the fornicator, flog each of them with a hundred stripes. Let not pity withhold you in their case, in a punishment prescribed by Allaah, if you believe in Allaah and the Last Day. And let a party of the believers witness their punishment”

[al-Noor 24:2 – interpretation of the meaning]

With regard to one who is married, the hadd punishment is execution. It says in a hadeeth narrated by Imam Muslim in his Saheeh (3199) that the Prophet (peace and blessings of Allaah be upon him) said: “For a married or previously-married person the punishment is one hundred lashes and stoning.” 

Secondly:

 Stealing is also a major sin. 

Allaah says (interpretation of the meaning): 

“And (as for) the male thief and the female thief, cut off (from the wrist joint) their (right) hands as a recompense for that which they committed, a punishment by way of example from Allaah”

[al-Maa’idah 5:38]

It was narrated from Ibn ‘Abbaas (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him) addressed the people of the Day of Sacrifice and said: “O people, what day is this?” They said, “A sacred day.” He said, “What land is this?” They said, “A sacred land.” He said, “What month is this?” They said, “A sacred month.” He said, “Your blood, your wealth and your honour are as sacred to you as this day of yours in this land of yours in this month of yours.” He repeated it several times, then he raised his head and said, “O Allaah, have I conveyed (the message)? O Allaah, have I conveyed (the message)?” Ibn ‘Abbaas (may Allaah be pleased with him) said: “By the One in Whose hand is my soul, this was his last advice to his ummah, so let those who are present convey it to those who are absent.” 

(Narrated by al-Bukhaari, 1652) 

The punishment for stealing is amputation of the right hand as is mentioned in the aayah quoted above. 

So we advise the one who is asking this question to repent and seek forgiveness for his sins. 

Allaah says (interpretation of the meaning): 

“And verily, I am indeed forgiving to him who repents, believes (in My Oneness, and associates none in worship with Me) and does righteous good deeds, and then remains constant in doing them (till his death)”

[Ta-Ha 20:82]

It was narrated that Anas ibn Maalik said: “I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: ‘Allaah says: “O son of Adam, so long as you call upon Me and ask of Me, I shall forgive you for what you have done, and I shall not mind. O son of Adam, were your sins to reach the clouds of the sky and were you then to ask forgiveness of Me, I would forgive you and I would not mind. O son of Adam, were you to come to Me with sins nearly as great as the earth and were you then to face Me, ascribing no partner to Me, I would bring you forgiveness nearly as great as it.”’” 

(al-Tirmidhi, 3540; classed as hasan by Shaykh al-Albaani in Saheeh al-Jaami’, 4338) 

It was narrated from Abu Dharr that the Prophet (peace and blessings of Allaah be upon him) said that Allaah says: “… O My slaves, you commit sin night and day, and I forgive all sins, so ask Me for forgiveness …”

(Muslim, 2577) 

Fourthly: 

Repentance that is a matter between a person and his Lord is better for him than confessing his sin before a qaadi (judge) so that the hadd punishment may be carried out on him. 

In Saheeh Muslim (1695) it is narrated that when Maa’iz came to the Messenger of Allaah (peace and blessings of Allaah be upon him) and said, “Purify me,” he said, “Woe to you! Go back and pray to Allaah for forgiveness and repent to Him.” 

Al-Haafiz Ibn Hajar said: 

It may be understood from this case – the case of Maa’iz when he confessed to having committed zina – that it is mustahabb for the one who falls into a similar sin to repent to Allaah and conceal his sin and not mention it to anyone, as Abu Bakr and ‘Umar said to Maa’iz. Whoever discovers anything of that nature should conceal it according to what we have mentioned; he should not expose it or refer the matter to the ruler, as the Prophet (peace and blessings of Allaah be upon him) said in this story: “If you had concealed it with your garment it would have been better for you.” Hence al-Shaafa’i (may Allaah be pleased with him) said: “If a person commits a sin and Allaah conceals it for him, I prefer for him to conceal it too and to repent,” and he quoted as evidence the story of Maa’iz with Abu Bakr and ‘Umar.

Fath al-Baari, 12/124, 125

 And Allaah knows best.