Du'a means supplication, and it is the act of calling upon Allah to ask for something.
The Prophet (ﷺ) said:
"Du'a is worship." [Abu Dawud].
In another hadeeth, the Prophet (ﷺ) said:
“Whoever does not ask Allah, The Exalted, He gets angry with him.” [At-Tirmithi]
We have been created needy so that we can turn with our needs to Allah, our Generous Creator. Through dua, we worship and connect to Him.
Like everything else in Islam, du'a has its proper way of going about it. There are a few basic conditions for acceptance of dua:
Your income and food are halal
As Muslims, we care how we earn and what we eat. Halal income means that it is earned using lawful means. The money must not be stolen or earned through haram means (e.g. selling alcohol). As for food, we make sure to consume halal products (especially meat) and stay away from haram substances.
Absolute certitude that Allah will answer your dua
Duas of all believers are answered in one of three ways as reported in a hadeeth of the Prophet (ﷺ):
“Every Muslim who makes a dua, which has nothing sinful and no breaking of family ties, will be granted by Allah one of three things:
Either Allah will give him a speedy answer, or store it up for him for the next world, or turn away from him an equivalent amount of evil.”
The companions then said: “We'll make a lot [of dua]!”, he (ﷺ) replied “Allah has more [than whatever you ask].”
Total focus on Allah while making dua
The dua must be sincere and the heart focused on the One being addressed.
Don’t ask Allah for something haram.
We don't ask for haram or bad things such as committing a sin, or dissevering family ties, or the right of another Muslim not to be fulfilled.
Don't make dua for something impossible.
There are different categories of impossible. Some things are impossible in principle, because they are a contradiction (e.g. a square circle), some are impossible to change because Allah has informed us about them (e.g. Pharaoh is destined to be in Hellfire), and some are not impossible in principle, but rather are customarily impossible due to the natural laws that have been set by Allah for this world (e.g. gravity).
Essentially, we ask for things that are possible in principle and don't contradict the truth.
There are many adab to strengthen your dua, we briefly mention some of them:
Choose the best time and place to make your dua (e.g. just before dawn (tahajjud), after the obligatory prayers, between adhan and iqamah).
Have wudu
Pray two rakaat of salat
Face the Qibla
Raise your hands
Say Alhamdulillah before and after the dua
Send salawat on the Prophet (blessings and peace be upon him) before, after, and in the middle of the dua
Before your dua make an absolute tawba from every sin
Give sadaqa
Ask for the greatest thing that you can conceive
Ask frequently
Ask of Allah by His most beautiful names.
Incorporate as many of the adaab as you can, and make some of them a habit.
Make sure to fulfill the conditions: halal income, certitude, presence of the heart, asking for good things.
Incorporate as many of the manners as you can.
Turn to Allah with all your needs.