Cold brew coffee can taste much different than coffee brewed with hot water. Why is this? It's actually all about chemistry, the reactions of the compounds in the coffee grounds with water. The video below by SciShow has an excellent description on how it works.
Some people like it more, others don't, it's all about personal preference. Luckily, you don't need any special equipment to try it out. Just mix some coffee grounds in water, and let it sit for a long time. It could be a few hours, or a day or so. Most people make it in the evening and let it sit in the refrigerator over night.
Use a coffee filter to separate the grounds, and you're done.
If you're just starting out, take 1/2 cup of ground coffee and put it in a glass (or mason jar). Fill with water (about a cup and a half) and let it set in the fridge over night. Make sure the grounds are saturated in the water.
When it is done, use a coffee filter to remove the grounds. I usually take my coffee brewer's basket, put at filter in it, and let it drain into another glass.
If you want it stronger, add more coffee and/or let it sit longer.