L'kovod the Hillula of the
Rebbe Reb Elimelech ben Reb Elazar Lipman of Lizensk ZY"A
In the Likutei Shoshana section of Noam Elimelech, we are given advice on how to get our prayers get answered.
It says in the Gemara (Gittin 7a): כל מי שיש לו צעקת לגימא על חבירו ודומם שוכן בסנה עושה לו דין "Anyone that has a complaint against their friend for taking away his livelihood and is silent, the One who dwells in the bush (Hashem) will make judgment".
One should always pray for his friend, because for oneself one can't pray successfully, as the Gemara (Berachos 5b) says:אין חבוש מתיר עצמו מבית האסורים "A prisoner can't free himself from prison". However, when praying for another, one can be answered speedily (as it says in Bava Kama 92a that if one prays for another's particular need, such as health, parnasa, shiduch, etc., and you need help in the same area, you will be answered first. See Segula to get Tefilos Answered). You should pray for your friend and your friend for you until everyone is answered. This is what the Gemara (Shevuos 39a) means: ישראל ערבים זה בזה. Simply this means "Yisroel are guarantors for each other", however ערבים can also mean "sweetening", as it says in Shir Hashirim (2:14) קולך ערב "the voice sweetens", since by praying for each other we are sweetening and consequently having the prayers answered.
The main prayer is in the "machshovah", meaning the mind, because this makes it easy for the prayers to be accepted since there is no "kitrug", the "accusing forces" aren't aware of the prayer. (This refers, of course, to additional prayers and supplications. It goes without saying that the standard prayers need to be said with the lips as described in Shulchan Aruch, although one should also think about what they're saying.) This is the explanation of the Gemara in Gittin that we started with: כל מי שיש לו צעקת לגימא על חבירו - whoever cries out in prayer for his friend who has no livelihood. ודומם – he is silent; he raises up his prayer in thought. שוכן בסנה עושה לו דין – Then Hashem will make judgment; He will answer the prayer for good.
The Noam Elimelech is teaching us that we should constantly be thinking about others, and through this advice above we will also be able to solve all of our difficulties.