How should they serve Hashem?
Radak: They should want what Hashem wants.
How should they serve Hashem with fear?
Radak: Fear Him, and know that He has power and strength, and not you, who come with a multitude of people.
What is the meaning of "v'Gilu bi'R'adah"?
Yuma 4b: In the place of Gilah (Rashi - Matan Torah, for "Pekudei Hashem Yesharim Mesamchei Lev" - 19:9), there will be trembling (Torah was received amidst fear).
Rashi: When the trembling will come - "Achazah Re'adah Chanefim" (Yeshayah 33:14), rejoice, if you served Hashem.
Radak: Do not be vexed due to my kingship - rejoice, for it is Hashem's desire. [Rejoice] with trembling [in front of Him].
Mesilas Yesharim (Perek 19): One must contemplate man's lowliness based on his physicality, and all the more so based on the sins one has done in his life. It is inevitable that one who tremble when he speaks in front of Hashem, and mentions His name and tries to be pleasing in front of Him.
Ya'aros Devash (2, Derush 5): One should rejoice on Rosh Hashanah, but with trembling 1 .
Malbim: If you serve Hashem with fear, later you will rejoice due to your trembling, that you feared His punishment.
An earlier source is a Teshuvah of R. Yitzchak ben Lev, brought in Oraisa 5756 8, edition 2, p.29.