The most basic dua is to recite:
Inna lilahi wa inna ilayhi raji'unMaulana Ashraf Ali Thanawi (ra) writes in Munaajaat al-Maqbool:
When something is lost:
"Itha Da'alahu shay-un aw abqa.It is also said that it is the experience of some people that reciting Surah 31 (Luqmaan), ayah 16 has the benefit of returning lost things:
Allahuma raadda-DDaalati wa * hadia-DDalaalati anta tahdi mina-DDalaalati urdud 'alayya Daalati biqudratika wa * sulTaanika fa innaha min 'aTaaika wa * faDlik."
"Oh Allah, the Returner of the lost and Guider of the misguided, You are the one who guides from misguidance, turn back towards me what I have lost with Your Power and Authority because it was Your own gift and bounty."
"Ya bunayya innaha in taku mithqala habbatimmin khardalin fatakun fee sakhratin aw fissamawati aw fil-ardi ya/ti biha Allahu innAllaha lateefun khabeer." (31:16)Maulana Ashraf Ali Thanawi (ra) also relates in A'mal Qurani that reciting the following verses will help:
"O my son!" (said Luqman), "If there be (but) the weight of a mustard-seed and it were (hidden) in a rock, or (anywhere) in the heavens or on earth, Allah will bring it forth: for Allah understands the finest mysteries, (and) is well-acquainted (with them). (31:16)
2:285-286As well as verses 7:54-56 with 9:128 added on to the end:
'inna rabbakumullahulladhee khalaqasamaawaati wal ardhi fee sittati ayyaa min thummastawaa 'alal 'arshi yughshilaylannahaara yatlubuhu hatheethauwashamsa wal qamara wanujuuma musakharaatin bi-amrihi alaalahulkhalqu wal amru tabaarakallahu rabbul 'alameen. (7:54)He also relates that Ja'far Khalidi lost a ring in the Tigris. He made this prayer:
ud 'oo rabbakum tadharru 'auwa khufyatah innahu laa yuhibbul mu'tadeen. (7:55)
walaatufsidoo fil ardhi ba'da islaahihaa wad 'oohu khayfauwa tama'an inna rahmatallahi qareebumminalmuhsineen. (7:56)
laqad jaa a kum rasooluminn anfusikum 'azeezun 'alayhi maa 'anittum hareedhun 'alaykum bilmumineena ra oo furraheem. (9:128)
"Your Guardian-Lord is Allah, Who created the heavens and the earth in six days, and is firmly established on the throne (of authority): He draweth the night as a veil o'er the day, each seeking the other in rapid succession: He created the sun, the moon, and the stars, (all) governed by laws under His command. Is it not His to create and to govern? Blessed be Allah, the Cherisher and Sustainer of the worlds!
Call on your Lord with humility and in private: for Allah loveth not those who trespass beyond bounds.
Do no mischief on the earth, after it hath been set in order, but call on Him with fear and longing (in your hearts): for the Mercy of Allah is (always) near to those who do good." (7:54-56)
"Now hath come unto you a Messenger from amongst yourselves: it grieves him that ye should perish: ardently anxious is he over you: to the Believers is he most kind and merciful." (9:128)
"yaa jaa mi 'annaasa liyau-millaa rayba fihi ijma' 'alayya dhaallati"and one day while looking through some papers he found the ring among them. It is also suggested to recite surah 93 (duha), repeat verse 7 thrice.
Heres an anecdote I found from SunniPath, attributed to Shaykh Abdul Qadir Gilani (ra):
According to a report from Ibn Tawus al-Yamani (may Allah the Exalted bestow His mercy upon him), his father, Tawus (may Allah the Exalted bestow His mercy upon him), told him:Hazrat 'Umar (ra) has also said:
"An Arab nomad [A'rabi] once came [to Mecca] on a riding camel of his. He caused the beast to kneel down, and hobbled its feet with a cord. Then he raised his head toward the sky, and said: 'O Allah, this riding camel, as well as the load upon its back, is covered by Your insurance, until I return to reclaim it.' He then went off and entered the Sacred Mosque [al-Masjid al-Haram].
"Some time later, the Arab nomad returned from the Sacred Mosque [al-Masjid al-Haram]–to find that the riding camel had been taken away, together with the load on its back. So he raised his head toward the sky, and said: 'O Allah, nothing has been stolen from me, for nothing is ever stolen except from You.' "
Tawus went on to say:
"While we were in this situation together with the Arab nomad, we suddenly caught sight of a man descending from the peak of Mount Abu Qubais. He was leading the riding camel with his left hand, while his right hand, which had been cut off, was attached to a cord around his neck. When he eventually reached the Arab nomad, he said: 'Here, take your riding camel, along with the load on its back.'
"I asked the man about his condition, so he explained: 'On the peak of Abu Qubais, I was approached by a rider on a gray horse. "O thief," he said to me, "hold out your hand!" So I held it out, and he placed it on a slab of rock. Then he took another piece of rock and used it to amputate my hand, which he then tied to my neck. "Now go back down the mountain," he told me, "and return the riding camel, along with the load it carries, to the Arab nomad."'"
'Umar [ibn al-Khattab] (may Allah be well pleased with him) used to quote these two verses [of Arabic poetry] as an instructive example:
Go easy on yourself, for the outcome of all affairs is determined by God's decree.
If something is meant to go elsewhere, it will never come your way, but if it is yours by destiny, from you it cannot flee.