Do not be anxious about anything, but in everything by prayer and supplication with thanksgiving let your requests be made known to God.
We are told to ask ‘in prayer,’ and I imagine this is so that we are setting aside time in which to approach God. Prayer is a considered activity, even those little arrow prayers in times of need; a direct route to God that He has set in place so that we can communicate with Him.
Supplication means to ask in a humble and sometimes earnest way. It is not only God we need to approach in this manner, this is the element of respect we should uphold at all times when dealing with one another. Humility is a strength exuded by those who are comfortable with themselves and have a healthy respect for others, regardless of their station in life. Many of the greatest people are known to be humble. We must be humble when approaching God... we are mortal and God is immortal therefore equality does not exist.
When asking God for anything we are told to give thanks. Within society we usually ask politely and say thank you when we receive something. I think that thanksgiving once again directs our attention to the Omnipotence of God and also encourages us to expect a positive answer. If we ask without expectation we basically undervalue ourselves. The other reason for giving thanks is that we are giving our requests to God and leaving them there while we focus on taking practical steps and wait for God to bless our efforts.
Remember, God is inclined to help those who help themselves.