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It is a mitzvah to run to the synagogue and to any other activity involving a mitzvah, as it is written, "Let us run in pursuit of the knowledge of G-d." Nevertheless, one should run only as far as the entrance of the Shul. In the Shul itself, by contrast, one should proceed with awe and fear.  ...  By contrast, when one leaves the synagogue, it is forbidden to run or to take large steps, because this implies that tarrying in the shul is a burden for him.

(The Alter Rebbe's Shulchan Oruch: sec. 90:13)

The miracle of Purim teaches us that prayer and repentance can open all doors and tear all decrees asunder. "Even after a decree is finalized, it is possible to annul it with prayer" (Rosh Hashana 16). "Tefillah is so powerful that is can change nature, save a person from danger and invalidate a guilty verdict" (Rabbeinu Bechaya on Tefillah).

On his fiftieth birthday, Reb Chaim Zelig Dobruskin had a yechidus with the Rebbe Rashab.
"I feel a marked difference in my davening and performance of Mitzvot. I lack the warmth that accompanied my service in my youthful days," he complained. "What do you expect, Chaim Zelig?" replied the Rebbe. "Fifty years of breakfasts and dinners take their toll on one's service of G-d."

Every individual, whether or not he has fulfilled his obligation to recite Shmone Esreh, must respond Amen after every single blessing. The intent he should have in mind is that "the blessing that was recited is true and I believe in it," for the word Amen signifies an affirmation of belief.  (The Alter Rebbe's Shulchan Oruch: sec. 124:9)

There is not the vaguest shadow of doubt that, wherever our feet tread, it is all in order to cleanse and purify the world with words of Torah and Tefillah. We, all of Israel, are emissaries of Hashem, each of us as Divine Providence has decreed for us. None of us is free from this sacred task placed on our shoulders.  (Hayom Yom  5 Adar 1 )

The Neshama, like the body, requires "food" and "clothes," except that the Neshama's food and clothes are spiritual: knowledge of the Torah is the "food" of the soul; the observance of the Mitzvot and the practice of good works in the daily life are the "garments" of the soul. 
(My Prayer)

Chassidim of Kotzk once asked the Rebbe Maharash why Lubavitcher Chassidim spend such a long time praying. They illustrated their question in parable form. "When one is riding through a village and hoodlums begin throwing stones at the carriage, is it not better to whip the horses and ride faster?" The Rebbe Maharash answered: "That would be the right thing to do, when the hoodlums are throwing stones from the outside."  "If, however, they have already entered the carriage, the only alternative is to stop the carriage and cast them off."
("Stories from my father's Shabbos table")

One may pray in any language he desires when he prays as part of a congregation. When, however, one prays individually, he should pray only in the Holy Tongue, for the ministering angels do not comprehend the other languages, and a person praying individually needs an angel as an intercessor, for his prayer to be accepted. By contrast, congregational prayer needs no intercessor.  (The Alter Rebbe's Shulchan Oruch: sec. 101:5)

Reb Elimelech of Lizhensk, before entering the shul to daven, would say: "Know where you are entering, what you will do there, Who is in this house, Whose house it is, and Who empowered you to enter this house."

One should not pray Shemoneh Esray in his heart alone. Rather, he should articulate the words with his lips and whisper audibly. He should not, however, make his voice heard (by someone standing more than four cubits away). A person who projects his voice during Shemoneh Esray is one of those whose faith is meager -- as if Hashem would not hear a whispered prayer.
(The Alter Rebbe's Shulchan Aruch 101:2)

The routine of the day begins with saying Modeh Ani. This is said before the morning washing of the hands, even while the hands are "impure". Because all the impurities in the world do not defile the "I acknowledge" of a Jew. He might lack one thing or another, but his Modeh Ani remains intact.  (Hayom Yom: Shvat 11)

"Rabbi Elazar said: A person should always pray, and not wait until trouble strikes. Reish Lakish said: Anyone who puts effort into his prayers down below will not have enemies in the upper realm."  (Sanhedrin 44b)

"In Chassidic Shuls, the words 'know before whom you stand' are not written above the amud, rather they are engraved in the mind and heart."
  (Likutei Diburim vol. 4)

"Tefillah can accomplish more than good deeds. Moshe Rabbeinu had more good deeds to his credit than any other human being, yet he was only granted his request in the merit of his prayers."  (Brochos 32)

The Tzemach Tzedek instructed all the tutors of his young grandchildren, that, in addition to regular studies, they should teach the simple meaning of the prayers. Once a month the children came to their grandfather to be tested in this subject.  (Hayom Yom 8 Teves)

The Alter Rebbe related:
"I was contemplating to myself where to go, and I could not decide . . .
I knew that in Vilna one can learn how to learn, and in Mezritch one can learn how to daven.  To learn I knew a little, and to daven I hardly knew, so I went to Mezritch."  (Sefer Ha'sichos תשײה pg. 132)