As we all who know Hebrew can assert, the sufix "im" in the words usually means plurality. How can HaShem be Elohim or Elokim if He is absolutely One and the Only Lord?
There are a lot of answers. Here are a couple:
In Hebrew, mastership is often expressed in the plural, as in אדוני יוסף or בעליו עמו. Similarly, then, the Name Elokim, which denotes that G-d is Master of the Universe, is in plural form (and sometimes even takes plural-form verbs). (Rashi to Gen. 20:13 and 35:7)
It's the plural of אלה, "these." This Name represents G-d as the master and controller of all of the disparate "these-es" of creation. (R' S.R. Hirsch to Gen. 1:1)
In a similar vein, though in Kabbalistic terms: Elokim is in plural form because it symbolizes the different spiritual worlds and levels which G-d created to serve as the conduits for His energy to reach the physical world and power it. (R' Shneur Zalman of Liadi, Torah Ohr, Vayera 56a ff)
כל לשון יש לו דרך כבוד. וכבוד ל' לועז שיאמר הקטן לנוכח הגדול לשון רבים. ובל' ישמעאל דרך כבוד שידבר הגדול כמו המלך בלשון רבים ובל' הקדש דרך כבוד לומר על הגדול ל' רבים כמו אדנים בעלים שאמרו אדנים קשה. ולקח בעליו.
Every language has an honorific mode. . . in Lashon Hakodesh the honorific mode is [expressed by] speaking about a superior in plural terms. . .
I like the analog to the English "royal we".
There are an abundance of answers given to this question, including those listed by Alex.
You might like the approach of Abarbanel, who sees no reason to assume that "elokim" is plural, since it is used as a name, like Ephraim, Mitzraim, or Chushim, which are all names in the "plural form". Rather he prefers the explanation that "elokim" is a composition of "el" meaning "god" in a general sense, and God's specific four-letter name ykv"k. (The me"m at the end of the name is to be grammatically correct in "closing off the word" so it won't sound like a possessive noun.)
R. Judah Halevi addresses this question right in the beginning of Part IV of the Kuzari:
The word has a plural form, because it was so used by gentile idolaters, who believed that every deity was invested with astral and other powers. Each of these was called Eloah; their united forces were therefore, called Elohim.
(Hirschfeld translation p. 198)
Apparently, then, the Torah uses the word Elohim because it conveys the idea of the sum of all powers, which is what God is, and not to impugn the unity of God.