There are a lot of options exist in the DVR market so you will need to decide which type of DVR you want to use. You can buy one that you will own and those are the most expensive or you can rent one from you cable or satellite company.
I recommend renting a DVR. It cost very little per month and gives you many features. Although it may not have as many features as the DVR's you buy.
After deciding which DVR you want you will need to install and configure it. The good news is if you rent one they will come out and configure it for you.
Now you simply start finding shows you want to record and start recording. You can even record all showings of a certain show. You can set your DVR to record your favorite TV series so you never miss one. You will have to make sure you watch and delete recorded shows to keep spare hard drive space available.
If you find you love the DVR, I recommend buying a DVR instead of the rental DVR. It will have hundreds of features that a rental doesn't.