Start by learning that genealogy has an a in it, then ...
You start with yourself and work your way back to your parents, their parents, etc. Talk to your relatives if possible, collect birth dates, birth locations, death dates, death locations, burial locations, full names, nick names, marriages, etc.
A genealogy software package has advantages especially once you get information on large numbers of people, but you don't need one to get started. There are also paper forms you can fill out for a family, one person's pedigree, etc.
If you live near where you and your recent ancestors lived you can use the courthouse, perhaps genealogy information in the local library.
Search engines on your surname(s) can be helpful but moreso if you have an unusual name (for Smith, Brown or Miller not so much).
There are many good genealogy web sites, some free, some by subscription.
It's very important to keep track of not only what you think you know, but the source of that information, because you will find conflicting information (census says he was 15 in 1910 and 28 in 1920).
Take your time. There's no hurry because you will never be done. Collect the data but seek to understand the individuals and the times they lived in. Do not judge. You might be descended form a governor but you're also probably descended from a horse thief. Maybe you get your sense of humor from the horse thief. Try to understand your ancestors in light of the time and place that they lived.
Keep in mind that there is much about the past that can never be learned, but especially early on you will likely be amazed at how much is known and is waiting for you to find it.