This short excerpt from Wikipedia briefly presents the various customs as to which Psalms are traditionally recited prior to the Grace After Meals on different days, including the Hebrew, English and transliterated texts below.
Preliminary Psalms
Psalm 126, Shir Hama’alot (Song of Ascents), which expresses the Jewish hope of return to Zion following their final redemption, is widely recited by Ashkenazi Jews before birkat hamazon on Shabbat, Jewish holidays and other days on which the penitential Tachanun prayer is not recited. This is frequently followed by reciting four further lines of four other Psalms, (145:21; 115:18; 118:1; 106:2), known as Tehillat Hashem (Praise of God). Less common is the recitation on weekdays of Psalm 137, Al Naharot Bavel (By the rivers of Babylon), which describes the reactions of the Jews in exile as would have been expressed during the Babylonian captivity. Some Spanish and Portuguese Jews precede Birkat HaMazon with Ein Keloheinu on Shabbat and holidays.
Shir Hama’alot – Song of Ascents (Psalm 126)
שִׁיר הַמַּעֲלוֹת בְּשׁוּב יְהוָה אֶת שִׁיבַת צִיּוֹן הָיִינוּ כְּחֹלְמִים. אָז יִמָּלֵא שְׂחוֹק פִּינוּ וּלְשׁוֹנֵנוּ רִנָּה אָז יֹאמְרוּ בַגּוֹיִם הִגְדִּיל יְהוָה לַעֲשׂוֹת עִם אֵלֶּה. הִגְדִּיל יְהוָה לַעֲשׂוֹת עִמָּנוּ הָיִינוּ שְׂמֵחִים. שׁוּבָה יְהוָה אֶת שְׁבִיתֵנוּ כַּאֲפִיקִים בַּנֶּגֶב. הַזֹּרְעִים בְּדִמְעָה בְּרִנָּה יִקְצֹרוּ. הָלוֹךְ יֵלֵךְ וּבָכֹה נֹשֵׂא מֶשֶׁךְ הַזָּרַע בֹּא יָבוֹא בְרִנָּה נֹשֵׂא אֲלֻמֹּתָיו.
On Sabbaths and Holy days, and on those days when Tachanun is not said, Psalm cxxvi. is said:
A Song of Degrees.—When the Lord turned again the captivity of Zion, we were like unto them that dream. Then was our mouth filled with laughter, and our tongue with exultation: then said they among the nations, The Lord hath done great things for them. The Lord hath done great things for us; whereat we rejoiced. Bring back our captivity, O Lord, as the streams in the south. They that sow in tears shall reap in joy. Though he goeth on his way weeping, bearing the store of seed, he shall come back with joy, bearing his sheaves.
Tehillat Hashem – Praise of God (145:21; 115:18; 118:1; 106:2)
תְּהִלַּת ה’ יְדַבֶּר פִּי וִיבָרֵךְ כָּל בָּשָׂר שֵׁם קָדְשׁוֹ לְעוֹלָם וָעֶד
My mouth will speak in praise of the Lord. Let every creature praise his holy name for ever and ever.
וַאֲנַחְנוּ נְבָרֵךְ יָהּ מֵעַתָּה וְעַד עוֹלָם הַלְלוּ יָהּ
But we will bless the Lord from this time forth and forevermore.
הוֹדוּ לַה’ כִּי טוֹב כִּי לְעוֹלָם חַסְדּוֹ
Oh, give thanks to the Lord, for He is good! For His mercy endures forever.
מִי יְמַלֵּל גְּבוּרוֹת ה’ יַשְׁמִיעַ כָּל תְּהִלָּתוֹ
Who can speak of the mighty deeds of the LORD, Or can show forth all His praise?
Al Naharot Bavel – By the Rivers of Babylon (Psalm 137)
עַל נַהֲרוֹת בָּבֶל שָׁם יָשַׁבְנוּ גַּם בָּכִינוּ בְּזָכְרֵנוּ אֶת צִיּוֹן. עַל עֲרָבִים בְּתוֹכָהּ תָּלִינוּ כִּנֹּרוֹתֵינוּ. כִּי שָׁם שְׁאֵלוּנוּ שׁוֹבֵינוּ דִּבְרֵי שִׁיר וְתוֹלָלֵינוּ שִׂמְחָה שִׁירוּ לָנוּ מִשִּׁיר צִיּוֹן. אֵיךְ נָשִׁיר אֶת שִׁיר יְהוָה עַל אַדְמַת נֵכָר. אִם אֶשְׁכָּחֵךְ יְרוּשָׁלִָם תִּשְׁכַּח יְמִינִי. תִּדְבַּק לְשׁוֹנִי לְחִכִּי אִם לֹא אֶזְכְּרֵכִי אִם לֹא אַעֲלֶה אֶת יְרוּשָׁלִַם עַל רֹאשׁ שִׂמְחָתִי. זְכֹר יְהוָה לִבְנֵי אֱדוֹם אֵת יוֹם יְרוּשָׁלִָם הָאֹמְרִים עָרוּ עָרוּ עַד הַיְסוֹד בָּהּ. בַּת בָּבֶל הַשְּׁדוּדָה אַשְׁרֵי שֶׁיְשַׁלֶּם לָךְ אֶת גְּמוּלֵךְ שֶׁגָּמַלְתְּ לָנוּ. אַשְׁרֵי שֶׁיֹּאחֵז וְנִפֵּץ אֶת עֹלָלַיִךְ אֶל הַסָּלַע.
By the rivers of Babylon, there we sat, sat and wept, as we thought of Zion. There on the poplars we hung up our lyres, for our captors asked us there for songs, our tormentors, for amusement, “Sing us one of the songs of Zion.” How can we sing a song of the LORD on alien soil? If I forget you, O Jerusalem, let my right hand wither; let my tongue stick to my palate if I cease to think of you, if I do not keep Jerusalem in memory even at my happiest hour. Remember, O LORD, against the Edomites the day of Jerusalem’s fall; how they cried, “Strip her, strip her to her very foundations!” Fair Babylon, you predator, a blessing on him who repays you in kind what you have inflicted on us; a blessing on him who seizes your babies and dashes them against the rocks!
Ein Keloheinu – There is None Like Our God
אין כאלהינו, אין כאדונינו
אין כמלכנו, אין כמושיענו.
מי כאלהינו, מי כאדונינו,
מי כמלכנו, מי כמושיענו.
נודה לאלהינו, נודה לאדונינו,
נודה למלכנו, נודה למושיענו.
ברוך אלהינו, ברוך אדונינו,
ברוך מלכנו, ברוך מושיענו.
אתה הוא אלהינו, אתה הוא אדונינו,
אתה הוא מלכנו,
אתה הוא מושיענו.
There is none like our God, There is none like our Lord,
There is none like our King, There is none like our Savior.
Who is like our God? Who is like our Lord?
Who is like our King? Who is like our Savior?
Let us thank our God, Let us thank our Lord,
Let us thank our King, Let us thank our Savior.
Blessed be our God, Blessed be our Lord,
Blessed be our King, Blessed be our Savior.
You are our God, You are our Lord,
You are our King,
You are our Savior.