One primary way to be happy on Shabbos is through singing zemiros. Singing songs on Shabbos is an old custom. The Gemara (Megillah 12:) states that at Achashveirosh's feast, the Jewish nation sang zemiros.
Tosfos (Sanhedrin 37: ד"ה מכנף) writes, "The Teshuvos HaGeonim writes that the people in Eretz Yisrael only say kedushah on Shabbos. This is because it states (Yeshayah 6:2), שש כנפים לאחד, that the malachim, the chayos hakodesh, have six wings, and with each wing, it sings a song on each day of the week. When Shabbos arrives, the chayos say to Hakadosh Baruch Hu, 'We don't have another wing with which to sing before You.' Hakadosh Baruch Hu replies, 'I have another wing, which will sing before Me. As it states (Yeshayah 24:16), מכנף הארץ זמירות שמענו, 'Songs will be heard from the wing that's upon the earth.'" This is referring to Bnei Yisrael, who sing songs to Hashem on Shabbos.
We can't begin to imagine the holiness of the malachim. Yet, on Shabbos, we take their place when we sing to Hashem. In fact, our songs are more precious to Hashem than the beautiful songs of the malachim.
The Chidushei HaRim (quoted in Sfas Emes, Vayikra, תרמ"ח) adds that singing is called כנף, wing, because with song we fly up to high levels.
Reb Shlomke Zvhiller zt'l said, "Every mitzvah one does on Shabbos is five hundred times greater than a mitzvah performed on a weekday. A daf Gemara studied on Shabbos is equivalent to studying five hundred daf Gemara on a weekday. A chapter of Tehillim on Shabbos equals five hundred chapters of Tehillim on a weekday." We understand that if one sings a zemer on Shabbos, it is like he sang five hundred songs. And if one sings for an hour on Shabbos, it is like he sang for five hundred hours!