Note that our Messenger (Peace be upon him) said:
... my comfort has been provided in prayer. (Sunan ibn Majah)
And he also said:
O Bilal, call iqamah for prayer: give us comfort by it. (Sunan abi Dawod)
So a starting point to perform a good prayer with much concentration is regarding it as a comfort, as a five times daily appointment where you can seek refuge by Allah and ask him and address him ...
For the concentration matter: I'd like to point at the following hadith (from Sunan ibn Majah)
It was narrated that Abu Ayyub said:
“A man came to the Prophet (ﷺ) and said: ‘O Messenger of Allah, teach me but make it concise.’
He said: ‘When you stand to pray, pray like a man bidding farewell. Do not say anything for which you will have to apologize. And give up hope for what other people have.’”
So one way to perform a good prayer is performing it as if it was the last prayer you would perform in your life. Think about it: How much emphasize would you put in it while you perform a dua' or how good would you try to recite the Quran, how much would you be concentrated in doing a very good job?
Among many examples of sahaba who practiced this here are two (note that this is my own translation take it with care):
It was narrated that al-Hussain ibn 'Ali (Peace be upon both of them), when he entering or beginning a prayer used to tremble and his face got a yellow coloring. When asked about it he used to say: Do you know in front of whom I'm now?
وكان الحسن بن علي رضي الله عنهما إذا دخل في الصلاة ارتعش واصفر لونه ... فإذا سئل عن ذلك قال : أتدرون بين يدي من أقوم الآن؟
While his father Imam 'Ali (May Allah be pleased with him) when he was performing ablution used to tremble. If asked about it he used to say: Now I bear the trust which the heavens and earth and mountains declined to bear it and feared it ... and I'm bearing it. (Referring to verse 33:72 )
وكان أبوه سيدنا علي رضي الله عنه إذا توضأ ارتجف فإذا سئل عن ذلك قال : الآن أحمل الأمانة التي عرضت على السماء والأرض والجبال فأبين أن يحملها وأشفقن منها .... وحملتها أنا
Also try to have in mind the qudsi Hadiths saying:
...Allah the Blessed, the Exalted, said, "I have divided the prayer into two halves between me and my slave. One half of it is for Me and one half of it is for My slave, and My slave has what he asks." ...
Which one may find in most Sunni hadith collection like al-Muwatta', among them a slightly different version in Sahih Muslim.
That means that if we perform a good and concentrated prayer we will be offered what we ask Allah.
Another point that helps on concentration is calmness (الطُّمأْنينة) as our Messenger (peace be upon him) taught the man who didn't pray well in the hadith. So one shouldn't hasten in the prayer as we've been warned in another hadith. And we are asked not to turn away, by looking right and left while praying as if we did Allah would stop looking upon us as stated in this hadith. Calmness means as the hadith suggests not to hasten so for example if we perform ruk'u, we shouldn't start reciting the dua' immediately until each part of our body has settled down in the right position ...
My major source in Arabic and also this fatwa in Arabic, a fatwa with an English translation on the same question but different wording.
And Allah knows best!