Ideally, it is believed that you want to keep your levels of triglycerides low and you want your levels of HDL high, and the size of your LDL large, since the small patterns are the dangerous ones. Finally, you want your ratio of total cholesterol divided by your HDL to be in the 3-5 range. You should easily be able to reach these goals through diet alone (exercise, too, if you'd like, cardio will help but all is good).
Dietary fat increases the size of your LDL and increases your HDL, which is what you want. On the other hand carbohydrates reduce the size of the LDL, which you want to avoid. So, avoid sugar and refined carbohydrates and eat more fats. Regarding fats, avoid trans fats and vegetable oils and instead go for long chain saturated and monosaturated fats (eggs, butter, steak, full fat cheese; bacon, olives, avocado).
Wait, I'd like to pick out some incorrect information for both the OP and you, JellyBaby.
Firstly, let me explain LDL and HDL. LDL - low density lipoproteins - are typically regarded as not very healthy. They deliver cholesterol and proteins from the liver to the rest of the body. HDL - high density lipoproteins - are typically regarded as healthy. They actually bring cholesterol and proteins back toward the liver, reducing serum cholesterol levels.
LDL consists of multiple types. There are large, buoyant LDLs which are generally regarded as less harmful than small, dense LDLs. Due to their size, large, buoyant LDLs actually have a harder time slipping into the lining of the blood vessels. Because of this, they can't as easily do damage to the blood vessels. However, small, dense LDLs can easily slip under the lining. Because of this, they can begin a cascade of vessel scarring, lipid formation, and potential thrombus formation. However, both are considered atherogenic (i.e. can cause narrowing of your blood vessels).
Saturated fat intake (typically taken in as animal fats from meat, cheese, cream, etc) increases both LDL and HDL. Sure, you need some saturated fat intake, but considering it is the most direct contributor to LDL levels, the amount you should take in shouldn't be that large. Monounsaturated (MUFAs) and polyunsaturated (PUFAs) fat intake from natural sources mainly work to increase HDL, which is great. Sources of MUFAs and PUFAs include olive oil, fish oil, fish, seeds, nuts, avocados, high quality meats (grass fed, cage free, etc), eggs. Soluble fiber intake (as found in beans, legumes, veggies, etc) actually decreases LDL. So the optimal diet would include moderate or moderate to low saturated fat intake (depending on how severe your hypercholesterolemia is), moderate to high intake of MUFAs and PUFAs (not from vegetable oils though), and moderate to high intake of fiber (specifically soluble fiber).
The point I'm trying to make is that JellyBaby entered some incorrect info, which has been propagated by many on the internet without my research to support it. Many proprietors of the Paleo and Atkin's diets say these things, but they haven't proven true whatsoever (specifically with regards to cholesterol. Some claims about weight loss are actually true). Saturated fat has regularly shown in nutrition, health, exercise phys, vascular, etc journals to increase risk of heart disease, atherosclerosis, etc as associated with increased LDL. Therefore, suggesting the OP increase saturated fats is a bad idea. Instead, he may want to lower saturated fats (depending on his intake now), increase MUFA/PUFA consumption, and increase fiber intake. In addition to this, aerobic exercise and losing weight (if you're overweight) are extremely important in modifying cholesterol in the best way possible. Aerobic exercise increases HDL and decreases LDL. I believe losing weight does the same.
I agree that refined carbohydrates may be detrimental to cholesterol levels, therefore your carb sources should be mainly from good, natural-form sources - sweet potatoes, beans, vegetable, potatoes, etc. Many refined products can increase your cholesterol, especially sugar. So keep away from those simple carbs and most importantly SUGAR.
The other info included from JellyBaby is quite frankly contrary to thousands of research articles. Full fat cheese, regular high-fat steak, butter are all poor choices if you're actually having an issue with your cholesterol. Like I said, you can have some, but don't get crazy. Your consumption of those can be counterproductive.