There are about a half dozen different Tessier lines in North America. The two largest are the descendents of Urbain Tessier -Lavigne or Mathurin Tessier. There are also a couple who were French immigrants directly to the US in the 1800s/1900s who aren't related (as far as we know) to any of the French-Canadian lines. If you can identify your ancestors who first came to the US, we can do our best to help you figure out which line you're part of and help you tap into the resources that can make your search easier.
With what you have right now, you might download to genealogy software from www.familysearch.org (it's freeware through the Mormon Church). Then start loading in all the info you know and linking as many people as you can. Interview your parents and members of their generation, as well as members of your grandparents' generation.
Even people who aren't directly related to you can be a great help. Elderly neighbors, local busy bodies, etc, are wonderful sources of info. They tend to remember who married whom, where people moved from, which churches they attended, etc. That can help tremendously when you go back before 1930. Until then, birth certificates weren't required and baptismal and Census records were the only thing telling you when family members came along. But if you can find the family parish, you can write to them requesting the baptismal records, as well as marriage and death records. But you need to do your own legwork first and have all the info you can organized so that you can ask for records from specific years (and months if you know them).
If you can get back to one of the Canadian lines, your job becomes pretty easy once you're back to 1799. The hardest part is getting enough info on that first ancestor who came to the US in order to link him to a town and a specific family in Canada. A few around here have taken years and years to make that linkup.
One other thing to find out is where people originally settled when they first came to the US. Emigrees tend to move en masse and resettle as a group. Even if you can't find your own ancestor's specific hometown, you can often narrow it down by finding others in the area who've traced their ancestors and go from there.
Hope it helps. Fill us in on whatever details (names/dates/parents/places) you can and we'll do our best to help you over the hurdles.