A lot of records in the States are intact, actually. The main census that was destroyed was for 1890. Otherwise, you have most of them logged, indexed and available online at Ancestry.com, which is owned by the Mormon church. They also have WW1 draft cards and lots of military records. I've tracked my family back quite a ways on many branches, some dating back 800 years. Some of it is conjecture, some educated guesses, lots of it based on other people's research. The main thing to do is have patience in looking.
I found that a lot of my research was just looking through census sheets. Page after page. What happens, is that you can often find your family. Then you can often also find families that your family married into living near them. I had this happen a lot. So, say you have, in my case, Katherin Anne Hollingsworth living with her family in the 1880 census, and living near and Oldham family. One of the male Oldhams married her. But one of the male Hollingsworths also married a female Oldham. Then, 20 years later, you can see the same families living near each other with new children. Also, if you're looking at an index of census data and it says to check page 18 or something, look 5 or 6 pages before and after that and scan for surnames you are looking for. You will often find errors in the index. And, ages are also often wrong. Sometimes the census dudes would come around on a farm, and the men would be out working on the farm. And maybe the women were busy with something and the kids answered the questions. They naturally think grandpa is much older than he is, and you can see this happen a lot. So don't rule out stuff based on exact data. Also, same happens with listing place of birth. Look for patterns where you can match an entire family even if something is slightly off.
Also, your surname may have a surname project. Mine does. And I used DNA testing to confirm that I am related to this guy, who brought my surname to the States in the 1680s.
Surname projects can be looked up here:
I'd recommend starting with searches at Ancestry.com. If you find records you want to actually view, you can either pay their membership, or you can view them at many of the family research libraries that the Church of Latter Day Saints has. They allow non members of the church to come in and use computers and people are also there to help you. It's pretty great.