It's an easy read in this translation.  Note that the nation of Israel was led at the time by God's prophet, Samuel, but they desired, instead, to be led by an earthly king.  Samuel called on God to guide him in answering the demand for a king brought to him by the elders of the tribe.  And God told Samuel that the people weren't rejecting Samuel's leadership; they were rejecting their God.  He told Samuel to describe to the people the nature of the king they had chosen, and then, if they still desired to live under that warlike ruler, to hearken to their demand, and give them what they wanted.

Most importantly, note that Samuel warned the people (verse 18), that if they suffered "buyer's remorse" later on, the Lord would not listen to their voices because they had ignored His warning.

This is good stuff, even if you're not a christian.

1 Samuel, chapter 8 (Revised Standard Edition):

1. When Samuel became old, he made his sons judges over Israel.
   
2. The name of his first-born son was Jo'el, and the name of his second, Abi'jah; they were judges in Beer-sheba.
   
3. Yet his sons did not walk in his ways, but turned aside after gain; they took bribes and perverted justice.
   
4. Then all the elders of Israel gathered together and came to Samuel at Ramah,
   
5. and said to him, "Behold, you are old and your sons do not walk in your ways; now appoint for us a king to govern us like all the nations."
   
6. But the thing displeased Samuel when they said, "Give us a king to govern us." And Samuel prayed to the LORD.
   
7. And the LORD said to Samuel, "Hearken to the voice of the people in all that they say to you; for they have not rejected you, but they have rejected me from being king over them.
   
8. According to all the deeds which they have done to me, from the day I brought them up out of Egypt even to this day, forsaking me and serving other gods, so they are also doing to you.
   
9. Now then, hearken to their voice; only, you shall solemnly warn them, and show them the ways of the king who shall reign over them."
   
10. So Samuel told all the words of the LORD to the people who were asking a king from him.
    
11. He said, "These will be the ways of the king who will reign over you: he will take your sons and appoint them to his chariots and to be his horsemen, and to run before his chariots;
    
12. and he will appoint for himself commanders of thousands and commanders of fifties, and some to plow his ground and to reap his harvest, and to make his implements of war and the equipment of his chariots.
    
13. He will take your daughters to be perfumers and cooks and bakers.
    
14. He will take the best of your fields and vineyards and olive orchards and give them to his servants.
    
15. He will take the tenth of your grain and of your vineyards and give it to his officers and to his servants.
    
16. He will take your menservants and maidservants, and the best of your cattle and your asses, and put them to his work.
    
17. He will take the tenth of your flocks, and you shall be his slaves.
    
18. And in that day you will cry out because of your king, whom you have chosen for yourselves; but the LORD will not answer you in that day."
    
19. But the people refused to listen to the voice of Samuel; and they said, "No! but we will have a king over us,
    
20. that we also may be like all the nations, and that our king may govern us and go out before us and fight our battles."