"Who may ascend the mountain of the Lord? Who may stand in his holy place?
The one who has clean hands and a pure heart, who does not trust in an idol
or swear by a false god."
(Psalm 24:3-4)

Before the answer is even given, the questions themselves lend you to believe that there is someone or some kind of person that can "ascend the mountain of the Lord" and "stand in His holy place". That belief is answered in the next verse with four criteria for ascension and standing. 
  1. Clean hands
  2. A pure heart
  3. No trust in an idol
  4. No swearing by a false god
The "mountain of the Lord" or hill as it is rendered in some translations seems to be most commonly connected with Jerusalem or Zion (Daniel 9:16; Daniel 9:20; Joel 2:1; Joel 3:17; Zephaniah 3:11). In the future God will raise this mount higher than anything on earth (Zechariah 14:10). And many from all nations will associate themselves with the Jews because of His favor upon their lives and land. 
  • "And many peoples and powerful nations will come to Jerusalem to seek the Lord Almighty and to entreat him. This is what the Lord Almighty says: 'In those days ten people from all languages and nations will take firm hold of one Jew by the hem of his robe and say, ‘Let us go with you, because we have heard that God is with you.’” (Zechariah 8:22-23)
Although Psalm 24:3-4 will be a literal, physical manifestation someday - I believe believers take this journey up the Hill of the Lord every time they pray. 

To me and my spirit Clean Hands speaks of coming to the Lord with a good service record, a good work ethic, not being lazy, working as unto the Lord and/or living right before the Lord. 

A Pure Heart means to have the right motives. Allow God to screen your thoughts, actions, and words before you think, do, or say them. A Pure Heart deals with intentions and the sincerity thereof. And a Pure Heart is concerned with integrity - what only God sees you doing and saying - it is what others don't see that goes a long way in making you a Champion for God.

Both the Idol and False god touch on the matters of focus and trust. God is a jealous God and has said so. "You are my witnesses," declares the LORD, "and my servant whom I have chosen, so that you may know and believe me and understand that I am he. Before me no god was formed, nor will there be one after me." (Isaiah 43:10) An idol is a physical thing or a habit that takes our focus away from our Friend. Paying attention to a false god gives the possibility that we will trust it with our needs instead of The Lover of Our Souls.

I encourage you and me to evaluate ourselves the next time we pray and certainly the next time we take Communion. Psalm 24:3-4 makes a statement within the questions posed. There is one who may ascend the mountain of the Lord. There is one who may stand in His holy place. However, do you meet the requirements of that one? Do you rest in Christ's righteousness and live in His ways? Is your life filled with decisions saturated with God's counseling? Have you kept your focus on Christ and trusted in Him as your Jehovah Jireh, God Your Provider? If you have done these things you will find that there is - A Hill Worth Climbing.