To the question “What to do with best thing in life?”, answer could well be “Enjoy it, certainly!” Even in Leviticus, there is some words to guide us on this matter. In our relatively modern day eyes, to know what Leviticus means is arduous since it was written for a society and religious community that is so different to ours.
Rather than wading through lot of materials that helps us with interpreting the text, let’s look at only a few things as we move to Leviticus 4:8-10. I’d suggest you read this section through several times, as before, noting words that catch your attention each time. You might identify some patterns, repeating words etc.
You will have different impression of the text from what I get. What I was interested in was the identification of kidneys, fat and such internal body elements. Actually, the description is rather gruesome. When was the last time you witness internal organs of any animal being butchered?

In fact, we are probably more familiar with things like mobile phone, travel ticket, and security keys to our house. As far as food is concerned, we are probably familiar with buying portion of fresh or frozen meat from the shop which we then cook at home to eat.
As we become less and less familiar with how meat is first sourced and eventually presented to us for eating, we are also finding description of the butchering process rather repulsive.
In the way we are more familiar with today’s ways of life, people of the day of Leviticus would be familiar with their kinds of life, and I’d saving butchering animals for food is not an activity necessarily ‘locked’ away so that very few people would know about it. In those days, if you want to stay alive, you probably need to know some basic skills in butchering in the first place.

What so important about the fat?
The fat is an indication of strength and healthiness of the animal. Too little fat is no good, too much fat also means the animal is becoming useless at work.
In today’s terms, having too much of something might mean being excessive with something, a kind of hoarding. This is the case when the items are kept for keeping sake, rather than put into their respective use.
The fat indicated here, around the kidneys etc, are the best kind of fat. Accumulation of such fat in the animal is an indication of good health. Other kinds of fat on the meat is not suitable for human to eat, these kind of fat at the organs need further treatment. It is this portion of fat that is being offered to God in the offering for forgiveness. As it is burned up, the sweat aroma pleases God.