Asking for help from Imam's (as)

وَمَا أَرْسَلْنَا مِن رَّسُولٍ إِلَّا لِيُطَاعَ بِإِذْنِ اللَّهِ وَلَوْ أَنَّهُمْ إِذ ظَّلَمُوا أَنفُسَهُمْ جَاءُوكَ فَاسْتَغْفَرُوا اللَّهَ وَاسْتَغْفَرَ لَهُمُ الرَّسُولُ لَوَجَدُوا اللَّهَ تَوَّابًا رَّحِيمًا"We sent not a messenger, but to be obeyed, in accordance with the will of Allah. If they had only, when they were unjust to themselves, come unto You and asked Allah's forgiveness, and the Messenger had asked forgiveness for them, they would have found Allah indeed Oft-returning, Most Merciful." [Quran 4:64]
The above verse clearly shows that Allah (swt), expects the believers to come to the Prophet (saww) for asking for forgiveness for their sins. This verse clearly permits us to Ask for help from the Prophet (saww).
And this is not limited to the life of the Prophet (saww). This verse is applicable even after the passing of Prophet Muhammad (saww) as proven from the following narration:
وروى السمعاني، عن أمير المؤمنين على بن أبى طالب عليه السلام أن أعرابيا جاء بعد ثلاثة أيام من دفن رسول الله صلى الله عليه وآله فرمى بنفسه على القبر الشريف، وحثا من ترابه على رأسه وقال: يا رسول الله قلت فسمعنا قولك، ووعيت عن الله فوعينا عنك، وكان فيما أنزله عليك (ولو أنهم إذ ظلموا أنفسهم جاءوك..) وقد ظلمت نفسي وجئتك تستغفر لي إلى ربي. فنودي من القبر أنه قد غفر لكAnd Narrated Al-Sam'aani from Amir Al-Momineen Ali bin Abi Talib (as):"That a Bedouin came three days after the burial of the Messenger of Allah (may Allah bless him and his family) and threw himself on the Holy grave and put the soil on his head and said, "O Messenger of Allah (saww), You said and we heard what you said. And you made us aware about Allah and We became aware about You. And it was revealed on you "If they had only, when they were unjust to themselves, come unto You...". I have wronged myself and have come to You, so pray for forgiveness for me to my Lord." Then came a call from the grave, verily He has forgiven you."
[Source: Al-Mazar - Shahid Al-Awwal, Pg. 4]
From Ziyarat-e-Jamiya

Ziyarat-e-Jamiya is an authentic Ziyarat truested and relied up by scholars from the past and present. This Ziyarat is also considered authentic by Sheikh Sadooq.

This Ziyarah can be recited for all the Imam's (as) and hence its called 'Jamiya'.

مُسْتَجِيرٌ بِكُمْ ‏زَائِرٌ لَكُمْ لاَئِذٌ عَائِذٌ بِقُبُورِكُمْ مُسْتَشْفِعٌ إِلَى اللَّهِ عَزَّ وَجَلَّ بِكُمْ وَمُتَقَرِّبٌ بِكُمْ إِلَيْهِ ‏وَمُقَدِّمُكُمْ أَمَامَ طَلِبَتِي وَحَوَائِجِي وَإِرَادَتِي

"I take shelter in your neighborhood. I make a visit to do homage and praise you. For me your resting abodes are sanctuaries. In the court of the Almighty you are my advocates. I seek His nearness through you. And submit to you(keep before you) the fulfillment of my wants and desire."

يَا وَلِيَّ اللَّهِ إِنَّ بَيْنِي وَبَيْنَ اللَّهِ عَزَّ وَجَلَّ ذُنُوباً لاَ يَأْتِي عَلَيْهَا إِلاَّ رِضَاكُمْ ‏فَبِحَقِّ مَنِ ائْتَمَنَكُمْ عَلَى سِرِّهِ وَاسْتَرْعَاكُمْ أَمْرَ خَلْقِهِ وَقَرَنَ طَاعَتَكُمْ بِطَاعَتِهِ ‏لَمَّا اسْتَوْهَبْتُمْ ذُنُوبِي وَكُنْتُمْ شُفَعَائِي

"Ya Wali Allah! Indeed there are sins between God - the mighty and tremendous - and me, that cannot be removed except by your pleasure; so by the one who has trusted you with His secret, and has made you shepherds in the affairs of His creation; and has conformed obeying you with obeying Him; seek the pardon of my sins; and you are my interceders." 

For the Imam's (as) that have passed away, we have the following words in the Ziyarat which prove that the status/position/authority/Wilayat of the Imam's (as) remains the same even after their death.

أَشْهَدُ أَنَّ هَذَا سَابِقٌ لَكُمْ فِيمَا مَضَى وَجَارٍ لَكُمْ فِيمَا بَقِيَ

"I testify that was was said earlier is for you in the past and will continue to be for your in the future."

[Source: Ziyarat-e-Jamiya, Uyoon Al-Akbar Al-Reza - Sheikh Sadooq]

For the details on the scholars who considered this Ziyarat as authentic and reliable read here (in arabic): http://www.alkafi.net/vb/showthread.php?t=460

Other than this, we have (at least) a couple of more Ziyarat with similar meaning hence making this Mutawaatir (frequently narrated). Those Ziyarat's are also quoted below.

Narrated from Mufazzal bin Amr from Aba Abdillah (as): 

روى المفضل بن عمر عن أبي عبد الله عليه السلام قال: إذا كانت لك حاجة إلى الله وصقت بها ذرعا، فصل ركعتين فإذا سلمت كبر الله ثلاثا، وسبح تسبيح فاطمة عليهاالسلام، ثم اسجد وقل مائة مرة: يا  مولاتیفاطمة أغيثيني، ثم ضع خدك الايمن علىالارض، وقل مثل ذلك، ثم عد إلى السجود وقل ذلك مائة مرة وعشر مرات واذكر حاجتك فإن الله يقضيها

Aba Abdillah (as) said:

"If you have a need from Allah (swt) and cannot reach it, then pray 2 Rakat (units). Then after Salaam, say "Allah is Great" 3 times, then recite the Tasbeeh of Fatema (sa), then go to Sajdah (Prostration) and say 100 times 'O My Master Fatema (sa), help me'. Then place your right cheek on the ground and say the same again. Then return to Sujood (Prostration) and say the same 110 times and then mention your need, verily Allah (swt) will fulfill it."

[Source: Bihar Al-Anwar Vol. 99, Pg. 254, Al-Balad al-Ameen Pg.159 - Actual source of this is the book 'Qabs Al-Misbah - Sheikh Al-Shehrasti]

Narrated from Abu Abdillah Imam Jafar Sadiq (as):

عن أبي عبدالله عليه السلام قال : إذا أردت زيارة الحسين عليه السلام فزره وأنتَ كَئيبٌ حَزين مَكروبٌ ، شُعثاً مغبراً جائعاً عَطْشاناً ، فإنَّ الحسين قُتِلَ حَزيناً مَكروباً شُعثاً مُغْبراً جائعاً عَطْشاناً ، وسَلْه الحوائج وانصرف عنه ، ولا تتّخِذْه وَطَناً

Abu Abdillah [Imam Sadiq (as)] said:

“When you want to go to the Ziyarah of Husain (as), go to his Ziyarah while you are saddened, anguished, grief-stricken, disheveled, covered with dust, hungry and thirsty for verily Husain (as) was killed while he was saddened, anguished, disheveled, covered with dust, hungry and thirsty.

(After you perform your Ziyarah), ask him for your needs and then leave. Do not settle in Karbala.

[Source: Al-Kafi Vol.4 Pg.587]

http://www.al-shia.org/html/ara/books/lib-hadis/al-kafi-4/22.htm#10

The following are the words from a Ziyarah of Imam Az-Zaman (atfs):

أسألك يا مولاي أن تسأل الله تبارك وتعالى في صلاح شأني ، وقضاء حوائجي ، وغفران ذنوبي ، والأخذ بيدي في ديني ودنياي وآخرتي لي ولاخواني وأخواتي المؤمنين والمؤمنات كافة ، إنه غفور رحيم

"I ask You, O My Master to ask the Almighty God for guidance in my matters, and fulfillment of my needs, and the forgiveness of my sins, and taking my hand in my religion and worldly affairs, and hereafter to me and my brothers and sisters all believing men and women, verily He (Allah)is Forgiving, Merciful."

[Source: Al Balad Al Ameen Pg. 286, Misbah Kafa'ami Pg. 497]

Here are the words from a Ziyarat to be recited in the month of Rajab. Its known as "Ziyarat e Rajabia"
This has come from the safeer of the 12th Imam (atfs) - Abul Qasim Al-Husain bin Rooh (ra)

Following is what we say to the Imam's (as) in this Ziyarat.

إني قصدتكم و اعتمدتكم بمسألتي و حاجتي و هي فكاك رقبتي من النار و المقر معكم في دار القرار مع شيعتكم الأبرار و السلام عليكم بما صبرتم فنعم عقبى الدار أنا سائلكم و آملكم فيما إليكم التفويض و عليكم التعويض فبكم يجبر المهيض و يشفى المريض

"I seek you, and depend upon you for my questions/issues and my needs and it is to safe my neck from the fire and make me stay with you in the house of award with your Shias. And peace be upon you .. I ask You and hope upon you in that what has been authorized to you and upon you is the compensation as from you and upon you is to cure the patient."

[Source: Misbah Al-Mutahajjid, Sheikh Toosi, Pg. 822]

Prayer for fulfillment of needs near the head of Imam Husain (as)

ما روي عن الصادق ع من كان له حاجة إلى الله عز و جل فليقف عند رأس الحسين ع و ليقل يا أبا عبد الله أشهد أنك تشهد مقامي و تسمع كلامي و إنك حي عند ربك ترزق فاسأل ربك و ربي في قضاء حوائجي 

Narrated from Imam Sadiq (as), "One who has a need from Allah (swt), then he is to stand near the head of Imam Husain (as) and say, "O Aba Abdillah (as), I testify that you are witnessing my position and hearing my words. Verily you are alive near your Lord receiving sustenance. Therefore ask Your Lord and my Lord for the fullfilment of my needs." 

[Source: Hidayat ul Wayi, Pg. 65]