Rasulullah 'alaihi Shalawatullah wa Salaam recite Du'a with "Allahummaghfirlii,"
Rasulullah 'alaihi Shalawatullah wa Salaam recite Ta'awwudz with "A'uudzu bi kalimatti taammaati... (I see Allah's refuge in Allah's perfect word...)."
Asking Allahu Tabaraka Ta'ala for granting our wishes.
Praising Allahu Ta'ala, for example:
Al Anbiya' (21):83 And Job, when he cried unto his Lord, (saying): Lo! adversity afflicteth me, and Thou art Most Merciful of all who show mercy.
Gathering the Muslimin and tell them to recite Du'a together. This is to be occasionally, not many.
An Nur (24):6 And for those who launch a charge against their spouses and have (in support) no evidence but their own their solitary evidence (can be received) if they bear witness four times (with an oath) by Allah that they are solemnly telling the truth; 2960
7 And the fifth (oath) (should be) that they solemnly invoke the curse (La'nat, Li'an) of Allah on themselves if they tell a lie.
8 But it would avert the punishment from the wife if she bears witness four times (with an oath) by Allah that (her husband) is telling a lie;
9 And the fifth (oath) should be that she solemnly invokes the wrath of Allah on herself if (her accuser) is telling the truth.
10 If it were not for Allah's grace and mercy on you and that Allah is Oft-Returning Full of Wisdom (ye would be ruined indeed).
Asking for rain to descend at some place.
Make a preferable choice then asking to Allahu 'Azza wa Jalla for making the decision whether the choice is good for the Din, life and him/herself.
Al Imran (3):61 And whoso disputeth with thee concerning him, after the knowledge which hath come unto thee, say (unto him): Come! We will summon our sons and your sons, and our women and your women, and ourselves and yourselves, then we will pray humbly (to our Lord) and (solemnly) invoke the curse of Allah upon those who lie.
According to Tawassul Anwaanuhu wa Ahkaamuhu by syaikh Abu Abdur Rahman Nashir Al Albaani, he putted the Hadits there, which shown that Tawassul consist of:
1. Telling an (alive) person, alive Muslim to recite Du'a to Allahu Jalla Jalaaluhu for granting our wish.
2. Using our Amal Shalih. Like saying "Allahumma, I have done a good deed, which I consider as the best good deeds of mine, and (tell the good deeds)..., if that made Thee pleased, then please save me from being captivate in this cave."
3. With Asma'ul Husna. For example: saying "Allahumma please make me love Thee, to love the poor people and to love the amal shalih (good deeds) which Thou love, verily Thou art Ghafuurul Waduud (Most Forgiving and Most Loving).
Keeping our wishes to Allahu Ta'ala inside our heart and never say "I had recite Du'a to Allahu Subhaanahu wa Ta'ala, but He ain't granting it."
Because Rasulullah 'alaihi Shalawatullah wa Salam said "Any person's Du'a is granted as long as they do not say 'Allah does not grant my Du'a'."(HR.Abu Daud, Shahih by syaikh Abu Abdurrahman Al Albaani).
Assalamu'alaikum wa rahmatullahi wa barakaatuh.