The morning zikr is said between fajr prayer and sunrise. The evening zikr is said after Asr prayer, but it is best to be said before Sunset.
`Abdullah bin Khubaib (May Allah be pleased with him) reported: The Messenger of Allah (PBUH) said to me
"Recite Surat Al-Ikhlas and Al-Mu`awwidhatain (Surat Al-Falaq and Surat An-Nas) three times at dawn and dusk. It will suffice you in all respects'' means that then one would not need any other recitation for the remembrance of Allah. Moreover, by virtue of these three Surah, Allah will protect the reciter from every dangerous thing. In other Ahadith, it is stated that after lying in the bed, the Prophet (PBUH) used to recite these Surah, then blow on his hands and rub them over his body to the extent he could. [Sahih el-Jami,#4406].
Shaddad ibn Aws reported that the Prophet said, "The best way to ask forgiveness is to say,
( اللَّهم أَنتَ ربِّي لا اِلهَ إلا أَنتَ، خَلَقتَنِي وأنا عَبدُكَ وأنا على عَهدِكَ و وَعدِكَ ما استَطَعتُ، أعوذُ بِكَ مِن شَرِّ ما صَنَعتُ أبُوءُ لَكَ بِنِعمَتِكَ عليَّ أبوءُ بِذَنبي فاغفِر لي فإنَّهُ لا يَغفِرُ الذنوبَ إلا أَنتَ )
'O Allah, You are my Lord. There is no god but You. You created me and I am Your slave. I comply with Your covenant and Your promise as much as I can. I seek refuge with you from the evil of what I have done. I acknowledge my sin, so forgive me. Only You can forgive sins.' Anyone who says it during the night having confidence in it and dies before morning will enter the Garden. Anyone who says this during the day having confidence in it and dies on that day before evening will enter the Garden. " [Sahih al-Bukhari]
Anas ibn Malik reported that the Messenger of Allah said, "If anyone says in the morning or the evening,
اللَّهم آني أصبحتُ(آو أمسيتُ) أُشهدُكَ وأُشهِدُ حَمَلَةَ عَرشِكَ ، وملائِكَتَكَ وجَميعَ خَلقِكَ، أَنَّكَ أنتَ اللهُ لا اِلهَ إلا أنتَ وَحدَكَ لا شريكَ لَكَ، وأنَّ محمدًا عَبدُكَ ورسولُكَ
'O Allah, I testify to You and I testify to the bearers of Your throne, Your angels and all Your creation that You are Allah and there is no god but You and Muhammad is Your slave and Messenger,' Allah will free a quarter of him from the fire. If anyone says it twice, Allah will free half of him from the Fire. If anyone says it three times, Allah will free three-quarters of him from the Fire. If anyone says it four times, Allah will free all of him from the Fire.'" [Reported by Abu Dawud, al-Bukhari, and it is hasan]
`Uthman bin `Affan (May Allah be pleased with him) reported: The Messenger of Allah (PBUH) said, "He who recites three times every morning and evening: ( بِسمِ الله الَّذي لا يَضُرُّ مع اسمِهِ شَيءٌ في الأرضِ ولا في السَماءِ وهُوَ السميعُ العليمُ)
`Bismillahil-ladhi la yadurru ma`as-mihi shai'un fil-ardi wa la fis-sama'i, wa Huwa as-Sami`ul-`Alim (In the Name of Allah with Whose Name there is protection against every kind of harm in the earth or in the heaven, and He is the All-Hearing and All-Knowing),' nothing will harm him.'' (at-Tirmidhi, Ahmed, isnad hasan)
Abu'd-Darda' said, "If anyone says in the morning and evening, (حسبيَ اللهُ لا إلَهَ إلا هُوَ عَلَيهِ تَوَكَلتُ وهوَ رَبُّ العَرشِ العَظيم)
'Allah is enough for me. There is no god but Him. I have relied on Him and He is the Lord of the Immense Throne' seven times, Allah will spare him what worries him (in this life and in the hereafter) ." (Abu Dawud, hadith Sahih)
'Abdullah ibn Ghannam al-Bayadi reported that the Messenger of Allah said, "If anyone says in the morning,
( اللَّهم ما أصبح(أمسي) بي مَن نِعمَةً أو بِأحَدٍ مِن خَلقِك فَمِنكَ وَحدَكَ لا شَريكَ لَكَ، فَلَكَ الحمدُ وَلَكَ الشُّكرُ) 'O Allah, whatever blessing comes to me or any of Your creation in the morning is from You alone with no partner; praise is Yours and thanks is to You' has fulfilled the thankfulness due for the day. If he says the like of that in the evening, he has fulfilled the thankfulness due for the night. " (Abu Dawud and an-Nasa'i, hadith hasan)
Thawban reported that the Prophet, peace be upon him, said, "If anyone says in the morning and in the evening,
(رَضيتُ بِالله ربَّاً، وبِالإسلامِ ديناً، وبِمُحمدٍ (ص) نَبيّاً )
'I am pleased with Allah as my Lord, with Islam as my religion, and with Muhammad as the Prophet,' Allah will certainly please him (at the day of judgement)." (Tirmizhi, who says it is a sound (hasan) hadith)
Abu'd-Darda' reported that the Messenger of Allah said, "Anyone who says the prayer on me ten times in the morning and ten times in the evening will obtain my intercession on the Day of Rising," [al-Tabarani, hasan]
Abu Hurayra reported that the Messenger of Allah said, "On the Day of Rising no one will bring anything better than someone who says in the morning and evening, 'Glory be to Allah and by His praise' a hundred times except someone who says the same as he says or more." In the version of Muslim, Tirmidhi, and Nasa'i, we find this addition: "Whoever says: subhan Allah wa bi hamdihi -- Glorified is Allah with all praise to Him -- a hundred times during a day, will have all his sins wiped off even if they were as numerous as the foam on the surface of the sea."
Abu Hurayra reported that the Prophet said: "Whoever says: (لا إله إلا الله وحده لا شريك له ،له الملك وله الحمد وهو على كل شيء قدير)
la ilaha illallahu wahdahu la sharika lah, lahu al-mulku wa lahu al-hamd, wa huwa `ala kulli shay'in qadir -- There is no god but Allah, alone, without partner. His is the sovereignty, and His the praise, and He has power over everything -- a hundred times a day will have a reward equivalent to the reward for freeing ten slaves. In addition, a hundred good deeds will be recorded for him and a hundred bad deeds of his will be wiped off, and it will be a safeguard for him from Satan that day until evening, and no one will be better in deeds than such a person except he who does more than that." (Narrated by Bukhari, Muslim)
At night only:
Ibn Mas`ud reported that the Prophet said: "If anyone recites the last two verses of Surat al- Baqara at night (2:285-286), they will suffice for him." (Narrated by Bukhari and Muslim). That is, these two verses will bring him a reward equivalent to that of a night prayer, and will safeguard him from any hurt during that night. Ibn Khuzayma in his Sahih mentioned it under the chapter "The Recitation of the Qur'an Equivalent in Reward to a Night Prayer."
Abu Hurairah (May Allah be pleased with him) reported: A man came to the Prophet (PBUH) and said, "What a trouble I suffered from a scorpion which stung me last night!'' He (PBUH) said, "Had you said in the evening:
( أعوذُ بكلماتِ اللهِ التامَّاتِ من شرِّ ما خلق )
`A`udhu bikalimatillahit-tammati min sharri ma khalaqa (I seek the protection of Allah's Perfect Words from the evil of whatever He has created),' it would not have harmed you.'' [Sahih Muslim].
For more information: please see the book: 'Husn al-Muslim'