You have High Triglycerides. So what do you do now?

A lipids-profile test is a common lab-blood test ordered by your medical doctor. A sample of your blood is withdrawn and sent to a laboratory for analysis. The results consist of: Total Cholesterol, LDL bad cholesterol, HDL good cholesterol, and triglycerides. There may be other results returned also, but these are the top four.
Lipids is another word for 'fats' and these top four are measurements of the fats of concern in your blood. Most likely if you had high triglycerides you also had high or low values for the other lipids. Ideally you would want the value for total cholesterol to be below 200 mg/dL; for HDL cholesterol above 40 mg/dL for women and above 50 mg/dL for men; and LDL cholesterol below 100 mg/dL.

Because if it is high it is an indication that you're eating too much and you're eating the wrong kinds of foods. Many people who eat fatty and sugary foods especially fast foods, have a tendency to be overweight. Being overweight can lead to a host of medical problems such as high cholesterol, heart disease manifesting itself in a heart attack or a stroke, and even type II diabetes. So your overall health and well being are at stake.
Physically you can develop joint problems since your bones have to support this extra weight. Your active life is limited and if you try to do a physical exercise you are more prone to injury. If you give up and resign yourself to a sedentary-inactive life, you will probably gain more weight and continue this unhealthy-downward cycle.

Glad you asked - it's quite simple. In order to lower your triglyceride level, you need to eat less fat, especially saturated fat. Saturated fat is found in butter and other animal fats, as well as palm and coconut oil.
And:
Eat lots of fruits, vegetables, and whole grains.
Buy lean meat and low-fat dairy products, such as low-fat cheese, yogurt, skim milk, and margarine instead of butter.
Reduce saturated fat to less than 10% of your daily calories, with your total fat intake being less than 30%.
Reduce fried foods to only a few servings per week. (Some alternatives to frying foods are grilling, broiling, steaming, and baking.)
Watch out for the trans fats which are found in many products (Salad dressings, baked desserts, creamy soups, and chocolate).
Become label savvy - review the Nutrition Facts Label on the products you buy.

Determine what a 'healthy' daily calorie count is for you. And start by eating as many calories as you burn. If you are eating too much, it is only common sense to cut back - consume fewer calories.
After you have control of the amount of food that you eat, then almost any low-fat diet full of fresh fruits and vegetables and lean cuts of meat or fish will help you bring down your triglyceride level.
Regular exercise will help you. Exercising for thirty minutes a day for five or more days a week will help you feel a lot better and lose weight at the same time. But remember to check with your medical doctor before starting a regular exercise program.

If I follow your suggestions and lower my triglycerides - what will happen to my cholesterol levels? Will they go up?

This is the good news - the answer is 'NO', total cholesterol will drop because the same eating habits that raised your triglycerides also raised your cholesterol. So following a sensible-low-fat diet will help you lower your cholesterol.