Cheesecake is one of those desserts that is notoriously difficult to make, simply because there are a lot of things that can go wrong during the process. To improve your chances of success, try using these tips:
- Opt for full-fat cream cheese in your recipe rather than using the reduced fat version. 
- Make sure that the cream cheese is at room temperature when you start making the recipe. This will help eliminate any lumps during the mixing process.
- Mix all of the ingredients besides the eggs together first, only adding the eggs in at the end. The more you mix the eggs, the more likely you are to get cracks in your cheesecake.
- Always make your cheesecake in a springform pan.
- Consider using a water bath when you make your cheesecake. In essence, this means placing the pan that holds the cheesecake inside another pan that is filled with water. The water helps ensure that the cheesecake is cooked gently, and also helps keep the surface moist which can minimize the risk of cracking. Just be sure to wrap the bottom of the pan that the cheesecake is being baked in with aluminum foil before placing it in the water. Otherwise, some water may leak in through the base of the springform pan. 
- Once the cheesecake is in the oven, don't open the door. Any cool air can increase the risk of cracks.
- Cool the cheesecake slowly after it is done cooking by turning off the oven and cracking the door. If you pull it out and cool it too quickly, it may crack.
In terms of how to make the actual cheesecake, this video has a recipe that sounds absolutely delicious. It also provides step-by-step instructions so that you can see exactly what you need to do:
The basic process starts by making a graham cracker crust using crushed graham crackers, sugar, and melted butter. This crust is pressed into the springform pan. The pan is then wrapped in aluminum foil to prepare it for the water bath.
Next the ingredients for the filling are mixed together with an electric mixer and added on top of the crust. The springform pan is then placed in a large roasting pan with enough hot water to reach about halfway up the side. Both pans are then placed in the oven and the cheesecake is baked. Once the time is up, the springform pan is removed and the cheesecake is chilled until it is time to serve it. Yum!